Non-zero |Ue3| and Quark-Lepton in Discrete Symmetry

YHAhn based on PhysRevD830760122011 with Hai-Yang Cheng and SCOh

2011-11-14

Non-zero |Ue3| and Quark-Lepton in Discrete Symmetry

YHAhn based on PhysRevD830760122011 with Hai-Yang Cheng and SCOh

2011-11-14

Double Chooz experiment sin2(2θ13)=0085plusmn0029(stat)plusmn0042(syst) 90CL

Outline

Present Knowledges and Motivations

Tri-Bimaximal Mixing and Non-zero |Ue3|

A4 symmetry+TBM and its Deviations in Seesaw

Charged fermion mixing angles

Low energy phenomenology and leptogenesis

Conclusion

2011-11-14

Present Knowledges and Motivations Neutrino oscillation (arXiv 1106 6028 GLFogli ELisi AMarroneAPalazzo AMRotunno)

Analysis by Fogli etal Including the latest T2K and MINOS results

Bi-Large mixing angles

These results should be compared with Theta13 which is very small

and with the quark mixing angles in the VCKM

Some new flavor symmetries

A clue to the nature among quark-lepton physics beyond SM

2011-11-14

Present Knowledges and Motivations Neutrino oscillation (arXiv 1106 6028 GLFogli ELisi AMarroneAPalazzo AMRotunno)

Analysis by Fogli etal Including the latest T2K and MINOS results

Bi-Large mixing angles

These results should be compared with Theta13 which is very small

and with the quark mixing angles in the VCKM

Some new flavor symmetries

A clue to the nature among quark-lepton physics beyond SM

2011-11-14

Present Knowledges and Motivations Neutrino oscillation (arXiv 1106 6028 GLFogli ELisi AMarroneAPalazzo AMRotunno)

Analysis by Fogli etal Including the latest T2K and MINOS results

Bi-Large mixing angles

These results should be compared with Theta13 which is very small

and with the quark mixing angles in the VCKM

Some new flavor symmetries

A clue to the nature among quark-lepton physics beyond SM

2011-11-14

The disparity that nature indicates between quark and lepton mixing angles has been viewed in terms of a quarkndashlepton complementarity which can be expressed in the relations ldquoRaidal 2004rdquo ldquoSmirnov and Minakatardquo

Present Knowledges and Motivations Neutrino oscillation (arXiv 1106 6028 GLFogli ELisi AMarroneAPalazzo AMRotunno)

Analysis by Fogli etal Including the latest T2K and MINOS results

Bi-Large mixing angles

These results should be compared with Theta13 which is very small

and with the quark mixing angles in the VCKM

Some new flavor symmetries

A clue to the nature among quark-lepton physics beyond SM

2011-11-14

The disparity that nature indicates between quark and lepton mixing angles has been viewed in terms of a quarkndashlepton complementarity which can be expressed in the relations ldquoRaidal 2004rdquo ldquoSmirnov and Minakatardquo

Accidental or not

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Dirac phase CP violation in ν oscillation Leptogenesis

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

1 2 CP

2011-11-14

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Dirac phase CP violation in ν oscillation Leptogenesis

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Dirac phase CP violation in ν oscillation Leptogenesis

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges Cosmological limit (including WMAP 3-years result)

upper bound on neutrino masses

(astro-ph0604335 Uros Seljak Anze Slosar Patrick McDonald)

Starting to disfavor the degenerate spectrum of neutrinos

BAU Astrophys J Suppl 192 (2011) 18

Why is there only Matter in Universe but no antimatter

bull No evidence of antimatter in our domain of Universe (~20Mpcasymp108light-years)

bull How can we generate ηB asymp10-10 from an initial condition for Big-Bang

2011-11-14

B 10of baryons(N )62

of photons1

)0

(NB

Non-zero |Ue3| and Quark-Lepton in Discrete Symmetry

YHAhn based on PhysRevD830760122011 with Hai-Yang Cheng and SCOh

2011-11-14

Double Chooz experiment sin2(2θ13)=0085plusmn0029(stat)plusmn0042(syst) 90CL

Outline

Present Knowledges and Motivations

Tri-Bimaximal Mixing and Non-zero |Ue3|

A4 symmetry+TBM and its Deviations in Seesaw

Charged fermion mixing angles

Low energy phenomenology and leptogenesis

Conclusion

2011-11-14

Present Knowledges and Motivations Neutrino oscillation (arXiv 1106 6028 GLFogli ELisi AMarroneAPalazzo AMRotunno)

Analysis by Fogli etal Including the latest T2K and MINOS results

Bi-Large mixing angles

These results should be compared with Theta13 which is very small

and with the quark mixing angles in the VCKM

Some new flavor symmetries

A clue to the nature among quark-lepton physics beyond SM

2011-11-14

Present Knowledges and Motivations Neutrino oscillation (arXiv 1106 6028 GLFogli ELisi AMarroneAPalazzo AMRotunno)

Analysis by Fogli etal Including the latest T2K and MINOS results

Bi-Large mixing angles

These results should be compared with Theta13 which is very small

and with the quark mixing angles in the VCKM

Some new flavor symmetries

A clue to the nature among quark-lepton physics beyond SM

2011-11-14

Present Knowledges and Motivations Neutrino oscillation (arXiv 1106 6028 GLFogli ELisi AMarroneAPalazzo AMRotunno)

Analysis by Fogli etal Including the latest T2K and MINOS results

Bi-Large mixing angles

These results should be compared with Theta13 which is very small

and with the quark mixing angles in the VCKM

Some new flavor symmetries

A clue to the nature among quark-lepton physics beyond SM

2011-11-14

The disparity that nature indicates between quark and lepton mixing angles has been viewed in terms of a quarkndashlepton complementarity which can be expressed in the relations ldquoRaidal 2004rdquo ldquoSmirnov and Minakatardquo

Present Knowledges and Motivations Neutrino oscillation (arXiv 1106 6028 GLFogli ELisi AMarroneAPalazzo AMRotunno)

Analysis by Fogli etal Including the latest T2K and MINOS results

Bi-Large mixing angles

These results should be compared with Theta13 which is very small

and with the quark mixing angles in the VCKM

Some new flavor symmetries

A clue to the nature among quark-lepton physics beyond SM

2011-11-14

The disparity that nature indicates between quark and lepton mixing angles has been viewed in terms of a quarkndashlepton complementarity which can be expressed in the relations ldquoRaidal 2004rdquo ldquoSmirnov and Minakatardquo

Accidental or not

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Dirac phase CP violation in ν oscillation Leptogenesis

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

1 2 CP

2011-11-14

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Dirac phase CP violation in ν oscillation Leptogenesis

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Dirac phase CP violation in ν oscillation Leptogenesis

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges Cosmological limit (including WMAP 3-years result)

upper bound on neutrino masses

(astro-ph0604335 Uros Seljak Anze Slosar Patrick McDonald)

Starting to disfavor the degenerate spectrum of neutrinos

BAU Astrophys J Suppl 192 (2011) 18

Why is there only Matter in Universe but no antimatter

bull No evidence of antimatter in our domain of Universe (~20Mpcasymp108light-years)

bull How can we generate ηB asymp10-10 from an initial condition for Big-Bang

2011-11-14

B 10of baryons(N )62

of photons1

)0

(NB

Outline

Present Knowledges and Motivations

Tri-Bimaximal Mixing and Non-zero |Ue3|

A4 symmetry+TBM and its Deviations in Seesaw

Charged fermion mixing angles

Low energy phenomenology and leptogenesis

Conclusion

2011-11-14

Present Knowledges and Motivations Neutrino oscillation (arXiv 1106 6028 GLFogli ELisi AMarroneAPalazzo AMRotunno)

Analysis by Fogli etal Including the latest T2K and MINOS results

Bi-Large mixing angles

These results should be compared with Theta13 which is very small

and with the quark mixing angles in the VCKM

Some new flavor symmetries

A clue to the nature among quark-lepton physics beyond SM

2011-11-14

Present Knowledges and Motivations Neutrino oscillation (arXiv 1106 6028 GLFogli ELisi AMarroneAPalazzo AMRotunno)

Analysis by Fogli etal Including the latest T2K and MINOS results

Bi-Large mixing angles

These results should be compared with Theta13 which is very small

and with the quark mixing angles in the VCKM

Some new flavor symmetries

A clue to the nature among quark-lepton physics beyond SM

2011-11-14

Present Knowledges and Motivations Neutrino oscillation (arXiv 1106 6028 GLFogli ELisi AMarroneAPalazzo AMRotunno)

Analysis by Fogli etal Including the latest T2K and MINOS results

Bi-Large mixing angles

These results should be compared with Theta13 which is very small

and with the quark mixing angles in the VCKM

Some new flavor symmetries

A clue to the nature among quark-lepton physics beyond SM

2011-11-14

The disparity that nature indicates between quark and lepton mixing angles has been viewed in terms of a quarkndashlepton complementarity which can be expressed in the relations ldquoRaidal 2004rdquo ldquoSmirnov and Minakatardquo

Present Knowledges and Motivations Neutrino oscillation (arXiv 1106 6028 GLFogli ELisi AMarroneAPalazzo AMRotunno)

Analysis by Fogli etal Including the latest T2K and MINOS results

Bi-Large mixing angles

These results should be compared with Theta13 which is very small

and with the quark mixing angles in the VCKM

Some new flavor symmetries

A clue to the nature among quark-lepton physics beyond SM

2011-11-14

The disparity that nature indicates between quark and lepton mixing angles has been viewed in terms of a quarkndashlepton complementarity which can be expressed in the relations ldquoRaidal 2004rdquo ldquoSmirnov and Minakatardquo

Accidental or not

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Dirac phase CP violation in ν oscillation Leptogenesis

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

1 2 CP

2011-11-14

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Dirac phase CP violation in ν oscillation Leptogenesis

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Dirac phase CP violation in ν oscillation Leptogenesis

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges Cosmological limit (including WMAP 3-years result)

upper bound on neutrino masses

(astro-ph0604335 Uros Seljak Anze Slosar Patrick McDonald)

Starting to disfavor the degenerate spectrum of neutrinos

BAU Astrophys J Suppl 192 (2011) 18

Why is there only Matter in Universe but no antimatter

bull No evidence of antimatter in our domain of Universe (~20Mpcasymp108light-years)

bull How can we generate ηB asymp10-10 from an initial condition for Big-Bang

2011-11-14

B 10of baryons(N )62

of photons1

)0

(NB

Present Knowledges and Motivations Neutrino oscillation (arXiv 1106 6028 GLFogli ELisi AMarroneAPalazzo AMRotunno)

Analysis by Fogli etal Including the latest T2K and MINOS results

Bi-Large mixing angles

These results should be compared with Theta13 which is very small

and with the quark mixing angles in the VCKM

Some new flavor symmetries

A clue to the nature among quark-lepton physics beyond SM

2011-11-14

Present Knowledges and Motivations Neutrino oscillation (arXiv 1106 6028 GLFogli ELisi AMarroneAPalazzo AMRotunno)

Analysis by Fogli etal Including the latest T2K and MINOS results

Bi-Large mixing angles

These results should be compared with Theta13 which is very small

and with the quark mixing angles in the VCKM

Some new flavor symmetries

A clue to the nature among quark-lepton physics beyond SM

2011-11-14

Present Knowledges and Motivations Neutrino oscillation (arXiv 1106 6028 GLFogli ELisi AMarroneAPalazzo AMRotunno)

Analysis by Fogli etal Including the latest T2K and MINOS results

Bi-Large mixing angles

These results should be compared with Theta13 which is very small

and with the quark mixing angles in the VCKM

Some new flavor symmetries

A clue to the nature among quark-lepton physics beyond SM

2011-11-14

The disparity that nature indicates between quark and lepton mixing angles has been viewed in terms of a quarkndashlepton complementarity which can be expressed in the relations ldquoRaidal 2004rdquo ldquoSmirnov and Minakatardquo

Present Knowledges and Motivations Neutrino oscillation (arXiv 1106 6028 GLFogli ELisi AMarroneAPalazzo AMRotunno)

Analysis by Fogli etal Including the latest T2K and MINOS results

Bi-Large mixing angles

These results should be compared with Theta13 which is very small

and with the quark mixing angles in the VCKM

Some new flavor symmetries

A clue to the nature among quark-lepton physics beyond SM

2011-11-14

The disparity that nature indicates between quark and lepton mixing angles has been viewed in terms of a quarkndashlepton complementarity which can be expressed in the relations ldquoRaidal 2004rdquo ldquoSmirnov and Minakatardquo

Accidental or not

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Dirac phase CP violation in ν oscillation Leptogenesis

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

1 2 CP

2011-11-14

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Dirac phase CP violation in ν oscillation Leptogenesis

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Dirac phase CP violation in ν oscillation Leptogenesis

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges Cosmological limit (including WMAP 3-years result)

upper bound on neutrino masses

(astro-ph0604335 Uros Seljak Anze Slosar Patrick McDonald)

Starting to disfavor the degenerate spectrum of neutrinos

BAU Astrophys J Suppl 192 (2011) 18

Why is there only Matter in Universe but no antimatter

bull No evidence of antimatter in our domain of Universe (~20Mpcasymp108light-years)

bull How can we generate ηB asymp10-10 from an initial condition for Big-Bang

2011-11-14

B 10of baryons(N )62

of photons1

)0

(NB

Present Knowledges and Motivations Neutrino oscillation (arXiv 1106 6028 GLFogli ELisi AMarroneAPalazzo AMRotunno)

Analysis by Fogli etal Including the latest T2K and MINOS results

Bi-Large mixing angles

These results should be compared with Theta13 which is very small

and with the quark mixing angles in the VCKM

Some new flavor symmetries

A clue to the nature among quark-lepton physics beyond SM

2011-11-14

Present Knowledges and Motivations Neutrino oscillation (arXiv 1106 6028 GLFogli ELisi AMarroneAPalazzo AMRotunno)

Analysis by Fogli etal Including the latest T2K and MINOS results

Bi-Large mixing angles

These results should be compared with Theta13 which is very small

and with the quark mixing angles in the VCKM

Some new flavor symmetries

A clue to the nature among quark-lepton physics beyond SM

2011-11-14

The disparity that nature indicates between quark and lepton mixing angles has been viewed in terms of a quarkndashlepton complementarity which can be expressed in the relations ldquoRaidal 2004rdquo ldquoSmirnov and Minakatardquo

Present Knowledges and Motivations Neutrino oscillation (arXiv 1106 6028 GLFogli ELisi AMarroneAPalazzo AMRotunno)

Analysis by Fogli etal Including the latest T2K and MINOS results

Bi-Large mixing angles

These results should be compared with Theta13 which is very small

and with the quark mixing angles in the VCKM

Some new flavor symmetries

A clue to the nature among quark-lepton physics beyond SM

2011-11-14

The disparity that nature indicates between quark and lepton mixing angles has been viewed in terms of a quarkndashlepton complementarity which can be expressed in the relations ldquoRaidal 2004rdquo ldquoSmirnov and Minakatardquo

Accidental or not

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Dirac phase CP violation in ν oscillation Leptogenesis

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

1 2 CP

2011-11-14

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Dirac phase CP violation in ν oscillation Leptogenesis

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Dirac phase CP violation in ν oscillation Leptogenesis

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges Cosmological limit (including WMAP 3-years result)

upper bound on neutrino masses

(astro-ph0604335 Uros Seljak Anze Slosar Patrick McDonald)

Starting to disfavor the degenerate spectrum of neutrinos

BAU Astrophys J Suppl 192 (2011) 18

Why is there only Matter in Universe but no antimatter

bull No evidence of antimatter in our domain of Universe (~20Mpcasymp108light-years)

bull How can we generate ηB asymp10-10 from an initial condition for Big-Bang

2011-11-14

B 10of baryons(N )62

of photons1

)0

(NB

Present Knowledges and Motivations Neutrino oscillation (arXiv 1106 6028 GLFogli ELisi AMarroneAPalazzo AMRotunno)

Analysis by Fogli etal Including the latest T2K and MINOS results

Bi-Large mixing angles

These results should be compared with Theta13 which is very small

and with the quark mixing angles in the VCKM

Some new flavor symmetries

A clue to the nature among quark-lepton physics beyond SM

2011-11-14

The disparity that nature indicates between quark and lepton mixing angles has been viewed in terms of a quarkndashlepton complementarity which can be expressed in the relations ldquoRaidal 2004rdquo ldquoSmirnov and Minakatardquo

Present Knowledges and Motivations Neutrino oscillation (arXiv 1106 6028 GLFogli ELisi AMarroneAPalazzo AMRotunno)

Analysis by Fogli etal Including the latest T2K and MINOS results

Bi-Large mixing angles

These results should be compared with Theta13 which is very small

and with the quark mixing angles in the VCKM

Some new flavor symmetries

A clue to the nature among quark-lepton physics beyond SM

2011-11-14

The disparity that nature indicates between quark and lepton mixing angles has been viewed in terms of a quarkndashlepton complementarity which can be expressed in the relations ldquoRaidal 2004rdquo ldquoSmirnov and Minakatardquo

Accidental or not

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Dirac phase CP violation in ν oscillation Leptogenesis

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

1 2 CP

2011-11-14

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Dirac phase CP violation in ν oscillation Leptogenesis

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Dirac phase CP violation in ν oscillation Leptogenesis

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges Cosmological limit (including WMAP 3-years result)

upper bound on neutrino masses

(astro-ph0604335 Uros Seljak Anze Slosar Patrick McDonald)

Starting to disfavor the degenerate spectrum of neutrinos

BAU Astrophys J Suppl 192 (2011) 18

Why is there only Matter in Universe but no antimatter

bull No evidence of antimatter in our domain of Universe (~20Mpcasymp108light-years)

bull How can we generate ηB asymp10-10 from an initial condition for Big-Bang

2011-11-14

B 10of baryons(N )62

of photons1

)0

(NB

Present Knowledges and Motivations Neutrino oscillation (arXiv 1106 6028 GLFogli ELisi AMarroneAPalazzo AMRotunno)

Analysis by Fogli etal Including the latest T2K and MINOS results

Bi-Large mixing angles

These results should be compared with Theta13 which is very small

and with the quark mixing angles in the VCKM

Some new flavor symmetries

A clue to the nature among quark-lepton physics beyond SM

2011-11-14

The disparity that nature indicates between quark and lepton mixing angles has been viewed in terms of a quarkndashlepton complementarity which can be expressed in the relations ldquoRaidal 2004rdquo ldquoSmirnov and Minakatardquo

Accidental or not

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Dirac phase CP violation in ν oscillation Leptogenesis

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

1 2 CP

2011-11-14

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Dirac phase CP violation in ν oscillation Leptogenesis

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Dirac phase CP violation in ν oscillation Leptogenesis

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges Cosmological limit (including WMAP 3-years result)

upper bound on neutrino masses

(astro-ph0604335 Uros Seljak Anze Slosar Patrick McDonald)

Starting to disfavor the degenerate spectrum of neutrinos

BAU Astrophys J Suppl 192 (2011) 18

Why is there only Matter in Universe but no antimatter

bull No evidence of antimatter in our domain of Universe (~20Mpcasymp108light-years)

bull How can we generate ηB asymp10-10 from an initial condition for Big-Bang

2011-11-14

B 10of baryons(N )62

of photons1

)0

(NB

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Dirac phase CP violation in ν oscillation Leptogenesis

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

1 2 CP

2011-11-14

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Dirac phase CP violation in ν oscillation Leptogenesis

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Dirac phase CP violation in ν oscillation Leptogenesis

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges Cosmological limit (including WMAP 3-years result)

upper bound on neutrino masses

(astro-ph0604335 Uros Seljak Anze Slosar Patrick McDonald)

Starting to disfavor the degenerate spectrum of neutrinos

BAU Astrophys J Suppl 192 (2011) 18

Why is there only Matter in Universe but no antimatter

bull No evidence of antimatter in our domain of Universe (~20Mpcasymp108light-years)

bull How can we generate ηB asymp10-10 from an initial condition for Big-Bang

2011-11-14

B 10of baryons(N )62

of photons1

)0

(NB

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Dirac phase CP violation in ν oscillation Leptogenesis

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Dirac phase CP violation in ν oscillation Leptogenesis

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges Cosmological limit (including WMAP 3-years result)

upper bound on neutrino masses

(astro-ph0604335 Uros Seljak Anze Slosar Patrick McDonald)

Starting to disfavor the degenerate spectrum of neutrinos

BAU Astrophys J Suppl 192 (2011) 18

Why is there only Matter in Universe but no antimatter

bull No evidence of antimatter in our domain of Universe (~20Mpcasymp108light-years)

bull How can we generate ηB asymp10-10 from an initial condition for Big-Bang

2011-11-14

B 10of baryons(N )62

of photons1

)0

(NB

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Dirac phase CP violation in ν oscillation Leptogenesis

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges Cosmological limit (including WMAP 3-years result)

upper bound on neutrino masses

(astro-ph0604335 Uros Seljak Anze Slosar Patrick McDonald)

Starting to disfavor the degenerate spectrum of neutrinos

BAU Astrophys J Suppl 192 (2011) 18

Why is there only Matter in Universe but no antimatter

bull No evidence of antimatter in our domain of Universe (~20Mpcasymp108light-years)

bull How can we generate ηB asymp10-10 from an initial condition for Big-Bang

2011-11-14

B 10of baryons(N )62

of photons1

)0

(NB

Present Knowledges and Motivations Nothing is known about all three CP-violating phases If δCP and θ13ne0 CP is violated in ν oscillations

δCP Not directly related to leptogenesis but would be likely in most leptogenesis models

Majorana phases Neutrinoless Double beta decay Leptogenesis

A relatively large Theta13gt0 (T2K and MINOS) opens up

CP-violation in neutrino oscillations Exps (T2K NOνAhellip)

Matter effects can experimentally determine the type of ν mass spectrum

normal or inverted mass ordering (goal of future LBL ν oscillation Exps program)

CP violations in the lepton sector are imperative if the baryon asymmetry of the

Universe (BAU) originated from leptogenesis scenario in the seesaw models

So any observation of the leptonic CP violation or demonstrating that CP is not a good

symmetry of the leptons can strengthen our belief in leptogenesis

1 2 CP

2011-11-14

Present Knowledges Cosmological limit (including WMAP 3-years result)

upper bound on neutrino masses

(astro-ph0604335 Uros Seljak Anze Slosar Patrick McDonald)

Starting to disfavor the degenerate spectrum of neutrinos

BAU Astrophys J Suppl 192 (2011) 18

Why is there only Matter in Universe but no antimatter

bull No evidence of antimatter in our domain of Universe (~20Mpcasymp108light-years)

bull How can we generate ηB asymp10-10 from an initial condition for Big-Bang

2011-11-14

B 10of baryons(N )62

of photons1

)0

(NB

Present Knowledges Cosmological limit (including WMAP 3-years result)

upper bound on neutrino masses

(astro-ph0604335 Uros Seljak Anze Slosar Patrick McDonald)

Starting to disfavor the degenerate spectrum of neutrinos

BAU Astrophys J Suppl 192 (2011) 18

Why is there only Matter in Universe but no antimatter

bull No evidence of antimatter in our domain of Universe (~20Mpcasymp108light-years)

bull How can we generate ηB asymp10-10 from an initial condition for Big-Bang

2011-11-14

B 10of baryons(N )62

of photons1

)0

(NB

Present Knowledges Cosmological limit (including WMAP 3-years result)

upper bound on neutrino masses

(astro-ph0604335 Uros Seljak Anze Slosar Patrick McDonald)

Starting to disfavor the degenerate spectrum of neutrinos

BAU Astrophys J Suppl 192 (2011) 18

Why is there only Matter in Universe but no antimatter

bull No evidence of antimatter in our domain of Universe (~20Mpcasymp108light-years)

bull How can we generate ηB asymp10-10 from an initial condition for Big-Bang

2011-11-14

B 10of baryons(N )62

of photons1

)0

(NB

All data can be explained in terms of oscillation between just 3 known species

Two possible orderings of neutrino masses

Earth matter

effects(LBL)

Quasi-Degenerate case

2011-11-14

Pontecorvo-Maki-NaKagawa-Sakata (PMNS) Matrix

Atmospheric and SBL reactor Solar and

LBL accelerator LBL reactor

Majorana phases Neutrinoless Double beta decay

23 23

13 13

13 1323

12 12

12 12

23

1 0 0 0 0

0 0 1 0 0

0 0 0 0 1

CP

CP

PMN

i

i

S

c s e

U P

s

c s

s c e c

c s

s c

2011-11-14

Goal sin22q13 ~ 002 90 CL in

3 years

Pontecorvo-Maki-NaKagawa-Sakata (PMNS) Matrix

Atmospheric and SBL reactor Solar and

LBL accelerator LBL reactor

Majorana phases Neutrinoless Double beta decay

23 23

13 13

13 1323

12 12

12 12

23

1 0 0 0 0

0 0 1 0 0

0 0 0 0 1

CP

CP

PMN

i

i

S

c s e

U P

s

c s

s c e c

c s

s c

2011-11-14

Goal sin22q13 ~ 002 90 CL in

3 years

Not observable

in oscillations

So far it is still unclear how to theoretically understand the observed neutrino mixing

A tentative way is to start with the data of ν oscillation and conjecture a simple

constant mixing pattern for example ldquoTri-Bimaximal mixingrdquo matrix

(Harrison Perkins and Scott

see also Wolfenstein(1970) and He and Zee)

It suggests that flavor structure for mixing should be divorced from trying to understand

the mass eigenvalues

Correlations between mass matrix elements It is suggestive of a flavor symmetry

2011-11-14

TBM diag

TBM T12

1

12

2

BM ( )

(

)

(

)

B

A B D

A B

A

m A B Dm

B

D

U U

So far it is still unclear how to theoretically understand the observed neutrino mixing

A tentative way is to start with the data of ν oscillation and conjecture a simple

constant mixing pattern for example ldquoTri-Bimaximal mixingrdquo matrix

(Harrison Perkins and Scott

see also Wolfenstein(1970) and He and Zee)

It suggests that flavor structure for mixing should be divorced from trying to understand

the mass eigenvalues

Correlations between mass matrix elements It is suggestive of a flavor symmetry

2011-11-14

TBM diag

TBM T12

1

12

2

BM ( )

(

)

(

)

B

A B D

A B

A

m A B Dm

B

D

U U

Tri-maximal Θ12=353O

So far it is still unclear how to theoretically understand the observed neutrino mixing

A tentative way is to start with the data of ν oscillation and conjecture a simple

constant mixing pattern for example ldquoTri-Bimaximal mixingrdquo matrix

(Harrison Perkins and Scott

see also Wolfenstein(1970) and He and Zee)

It suggests that flavor structure for mixing should be divorced from trying to understand

the mass eigenvalues

Correlations between mass matrix elements It is suggestive of a flavor symmetry

2011-11-14

TBM diag

TBM T12

1

12

2

BM ( )

(

)

(

)

B

A B D

A B

A

m A B Dm

B

D

U U

So far it is still unclear how to theoretically understand the observed neutrino mixing

A tentative way is to start with the data of ν oscillation and conjecture a simple

constant mixing pattern for example ldquoTri-Bimaximal mixingrdquo matrix

(Harrison Perkins and Scott

see also Wolfenstein(1970) and He and Zee)

It suggests that flavor structure for mixing should be divorced from trying to understand

the mass eigenvalues

Correlations between mass matrix elements It is suggestive of a flavor symmetry

If there exists such a flavor symmetry in Nature the TBM pattern for the neutrino mixing will be a good zeroth order approximation to real world

2011-11-14

TBM diag

TBM T12

1

12

2

BM ( )

(

)

(

)

B

A B D

A B

A

m A B Dm

B

D

U U

Deviations from Tri-Bimaximal It is clear by now that the TBM is not consistent with the recent experimental data

on the reactor mixing angle θ13 because of the vanishing matrix element Ue3 in UTBM

(arXiv 11066028 GLFogli E Lisi A Marrone A Palazzo and AM Rotunno)

Recent data of the T2K Collaboration and the analysis based on global fits of neutrino

oscillations enter into a new phase of precise measurements of the neutrino mixing angles

and mass-squared differences indicating that the TBM mixing for three flavors of leptons

should be modified 2011-11-14

Seesaw A simple and attractive explanation of the smallness of ν mass Origin of operator

SEESAW MECHANISM

(i) SM+RH ν (EW singlet) (Minkowski 1977)

(ii) SM+SU(2) Triplet Higgs (KonetschnvKummer 1977)

(iii) SM+SU(2) Triplet fermions (RFoot HLew X-G He GC Joshi 1989)

while Ł of the EW int keeps invariant SU(2)timesU(1)

3times3 Seesaw model has 18 parameters 12 real+6 phases (cf Casas Ibarra )

Integrating out the heavy fermions leaves us with observable mass matrix

(9 observables 6 real+3 phases) Half of the parameters of the model get lost at low-E

The 3 low-E CP-violating depend in general on all 6 seesaw phases

The effects of high-E CP-violating phases control the generation of the BAU in the

leptogenesis scenario in |ltmgt| and in the leptonic CP-violating rephasing invariant Jcp

Complicated amp many unknown parameters

2011-11-14

B L

d d

D PMNS RY U m R M

Flavor Symmetry In approaches to reconstruct the high-energy physics from low-energy data

one can assume a flavor symmetry which may reduce the unknown parameters in leading order

For example CKM matrix=Identity+Corrections

PMNS matrix= TBM+Corrections

Unless flavor symmetries are assumed particle masses and mixings are generally

undetermined in gauge theory

A4 S4S3Trsquohelliphellip

Symmetry observed patterns of

Breaking fermion masses and mixings

2011-11-14

Why A4 symmetry To understand the present data we consider A4 flavor symmetry

(EMa and GRajarasekaran GAltarelly and FFeruglio XGHe YYKeum and RVolkas)

Tri-Bimaximal in neutrino mixing amp No Quark mixing

as a good approximation in leading order

Non-zero |Ue3| and correct CKM matrix Higher order corrections

In seesaw + A4

Leptogenesis scale ~ 1013-1015 GeV due to the equal size of moduli of

neutrino Yukawa couplings (strong wash-out)

Without the aid of higher order corrections or soft-breaking term

non-zero |Ue3| as well as Leptogenesis are not possible

TeV-scale Resonant-Leptogenesis

2011-11-14

Why A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

1

3

4

2

A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

A4 Symmetry

Letrsquos denote two A4 triplets and

where

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Pontecorvo-Maki-NaKagawa-Sakata (PMNS) Matrix

Atmospheric and SBL reactor Solar and

LBL accelerator LBL reactor

Majorana phases Neutrinoless Double beta decay

23 23

13 13

13 1323

12 12

12 12

23

1 0 0 0 0

0 0 1 0 0

0 0 0 0 1

CP

CP

PMN

i

i

S

c s e

U P

s

c s

s c e c

c s

s c

2011-11-14

Goal sin22q13 ~ 002 90 CL in

3 years

Pontecorvo-Maki-NaKagawa-Sakata (PMNS) Matrix

Atmospheric and SBL reactor Solar and

LBL accelerator LBL reactor

Majorana phases Neutrinoless Double beta decay

23 23

13 13

13 1323

12 12

12 12

23

1 0 0 0 0

0 0 1 0 0

0 0 0 0 1

CP

CP

PMN

i

i

S

c s e

U P

s

c s

s c e c

c s

s c

2011-11-14

Goal sin22q13 ~ 002 90 CL in

3 years

Not observable

in oscillations

So far it is still unclear how to theoretically understand the observed neutrino mixing

A tentative way is to start with the data of ν oscillation and conjecture a simple

constant mixing pattern for example ldquoTri-Bimaximal mixingrdquo matrix

(Harrison Perkins and Scott

see also Wolfenstein(1970) and He and Zee)

It suggests that flavor structure for mixing should be divorced from trying to understand

the mass eigenvalues

Correlations between mass matrix elements It is suggestive of a flavor symmetry

2011-11-14

TBM diag

TBM T12

1

12

2

BM ( )

(

)

(

)

B

A B D

A B

A

m A B Dm

B

D

U U

So far it is still unclear how to theoretically understand the observed neutrino mixing

A tentative way is to start with the data of ν oscillation and conjecture a simple

constant mixing pattern for example ldquoTri-Bimaximal mixingrdquo matrix

(Harrison Perkins and Scott

see also Wolfenstein(1970) and He and Zee)

It suggests that flavor structure for mixing should be divorced from trying to understand

the mass eigenvalues

Correlations between mass matrix elements It is suggestive of a flavor symmetry

2011-11-14

TBM diag

TBM T12

1

12

2

BM ( )

(

)

(

)

B

A B D

A B

A

m A B Dm

B

D

U U

Tri-maximal Θ12=353O

So far it is still unclear how to theoretically understand the observed neutrino mixing

A tentative way is to start with the data of ν oscillation and conjecture a simple

constant mixing pattern for example ldquoTri-Bimaximal mixingrdquo matrix

(Harrison Perkins and Scott

see also Wolfenstein(1970) and He and Zee)

It suggests that flavor structure for mixing should be divorced from trying to understand

the mass eigenvalues

Correlations between mass matrix elements It is suggestive of a flavor symmetry

2011-11-14

TBM diag

TBM T12

1

12

2

BM ( )

(

)

(

)

B

A B D

A B

A

m A B Dm

B

D

U U

So far it is still unclear how to theoretically understand the observed neutrino mixing

A tentative way is to start with the data of ν oscillation and conjecture a simple

constant mixing pattern for example ldquoTri-Bimaximal mixingrdquo matrix

(Harrison Perkins and Scott

see also Wolfenstein(1970) and He and Zee)

It suggests that flavor structure for mixing should be divorced from trying to understand

the mass eigenvalues

Correlations between mass matrix elements It is suggestive of a flavor symmetry

If there exists such a flavor symmetry in Nature the TBM pattern for the neutrino mixing will be a good zeroth order approximation to real world

2011-11-14

TBM diag

TBM T12

1

12

2

BM ( )

(

)

(

)

B

A B D

A B

A

m A B Dm

B

D

U U

Deviations from Tri-Bimaximal It is clear by now that the TBM is not consistent with the recent experimental data

on the reactor mixing angle θ13 because of the vanishing matrix element Ue3 in UTBM

(arXiv 11066028 GLFogli E Lisi A Marrone A Palazzo and AM Rotunno)

Recent data of the T2K Collaboration and the analysis based on global fits of neutrino

oscillations enter into a new phase of precise measurements of the neutrino mixing angles

and mass-squared differences indicating that the TBM mixing for three flavors of leptons

should be modified 2011-11-14

Seesaw A simple and attractive explanation of the smallness of ν mass Origin of operator

SEESAW MECHANISM

(i) SM+RH ν (EW singlet) (Minkowski 1977)

(ii) SM+SU(2) Triplet Higgs (KonetschnvKummer 1977)

(iii) SM+SU(2) Triplet fermions (RFoot HLew X-G He GC Joshi 1989)

while Ł of the EW int keeps invariant SU(2)timesU(1)

3times3 Seesaw model has 18 parameters 12 real+6 phases (cf Casas Ibarra )

Integrating out the heavy fermions leaves us with observable mass matrix

(9 observables 6 real+3 phases) Half of the parameters of the model get lost at low-E

The 3 low-E CP-violating depend in general on all 6 seesaw phases

The effects of high-E CP-violating phases control the generation of the BAU in the

leptogenesis scenario in |ltmgt| and in the leptonic CP-violating rephasing invariant Jcp

Complicated amp many unknown parameters

2011-11-14

B L

d d

D PMNS RY U m R M

Flavor Symmetry In approaches to reconstruct the high-energy physics from low-energy data

one can assume a flavor symmetry which may reduce the unknown parameters in leading order

For example CKM matrix=Identity+Corrections

PMNS matrix= TBM+Corrections

Unless flavor symmetries are assumed particle masses and mixings are generally

undetermined in gauge theory

A4 S4S3Trsquohelliphellip

Symmetry observed patterns of

Breaking fermion masses and mixings

2011-11-14

Why A4 symmetry To understand the present data we consider A4 flavor symmetry

(EMa and GRajarasekaran GAltarelly and FFeruglio XGHe YYKeum and RVolkas)

Tri-Bimaximal in neutrino mixing amp No Quark mixing

as a good approximation in leading order

Non-zero |Ue3| and correct CKM matrix Higher order corrections

In seesaw + A4

Leptogenesis scale ~ 1013-1015 GeV due to the equal size of moduli of

neutrino Yukawa couplings (strong wash-out)

Without the aid of higher order corrections or soft-breaking term

non-zero |Ue3| as well as Leptogenesis are not possible

TeV-scale Resonant-Leptogenesis

2011-11-14

Why A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

1

3

4

2

A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

A4 Symmetry

Letrsquos denote two A4 triplets and

where

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Pontecorvo-Maki-NaKagawa-Sakata (PMNS) Matrix

Atmospheric and SBL reactor Solar and

LBL accelerator LBL reactor

Majorana phases Neutrinoless Double beta decay

23 23

13 13

13 1323

12 12

12 12

23

1 0 0 0 0

0 0 1 0 0

0 0 0 0 1

CP

CP

PMN

i

i

S

c s e

U P

s

c s

s c e c

c s

s c

2011-11-14

Goal sin22q13 ~ 002 90 CL in

3 years

Not observable

in oscillations

So far it is still unclear how to theoretically understand the observed neutrino mixing

A tentative way is to start with the data of ν oscillation and conjecture a simple

constant mixing pattern for example ldquoTri-Bimaximal mixingrdquo matrix

(Harrison Perkins and Scott

see also Wolfenstein(1970) and He and Zee)

It suggests that flavor structure for mixing should be divorced from trying to understand

the mass eigenvalues

Correlations between mass matrix elements It is suggestive of a flavor symmetry

2011-11-14

TBM diag

TBM T12

1

12

2

BM ( )

(

)

(

)

B

A B D

A B

A

m A B Dm

B

D

U U

So far it is still unclear how to theoretically understand the observed neutrino mixing

A tentative way is to start with the data of ν oscillation and conjecture a simple

constant mixing pattern for example ldquoTri-Bimaximal mixingrdquo matrix

(Harrison Perkins and Scott

see also Wolfenstein(1970) and He and Zee)

It suggests that flavor structure for mixing should be divorced from trying to understand

the mass eigenvalues

Correlations between mass matrix elements It is suggestive of a flavor symmetry

2011-11-14

TBM diag

TBM T12

1

12

2

BM ( )

(

)

(

)

B

A B D

A B

A

m A B Dm

B

D

U U

Tri-maximal Θ12=353O

So far it is still unclear how to theoretically understand the observed neutrino mixing

A tentative way is to start with the data of ν oscillation and conjecture a simple

constant mixing pattern for example ldquoTri-Bimaximal mixingrdquo matrix

(Harrison Perkins and Scott

see also Wolfenstein(1970) and He and Zee)

It suggests that flavor structure for mixing should be divorced from trying to understand

the mass eigenvalues

Correlations between mass matrix elements It is suggestive of a flavor symmetry

2011-11-14

TBM diag

TBM T12

1

12

2

BM ( )

(

)

(

)

B

A B D

A B

A

m A B Dm

B

D

U U

So far it is still unclear how to theoretically understand the observed neutrino mixing

A tentative way is to start with the data of ν oscillation and conjecture a simple

constant mixing pattern for example ldquoTri-Bimaximal mixingrdquo matrix

(Harrison Perkins and Scott

see also Wolfenstein(1970) and He and Zee)

It suggests that flavor structure for mixing should be divorced from trying to understand

the mass eigenvalues

Correlations between mass matrix elements It is suggestive of a flavor symmetry

If there exists such a flavor symmetry in Nature the TBM pattern for the neutrino mixing will be a good zeroth order approximation to real world

2011-11-14

TBM diag

TBM T12

1

12

2

BM ( )

(

)

(

)

B

A B D

A B

A

m A B Dm

B

D

U U

Deviations from Tri-Bimaximal It is clear by now that the TBM is not consistent with the recent experimental data

on the reactor mixing angle θ13 because of the vanishing matrix element Ue3 in UTBM

(arXiv 11066028 GLFogli E Lisi A Marrone A Palazzo and AM Rotunno)

Recent data of the T2K Collaboration and the analysis based on global fits of neutrino

oscillations enter into a new phase of precise measurements of the neutrino mixing angles

and mass-squared differences indicating that the TBM mixing for three flavors of leptons

should be modified 2011-11-14

Seesaw A simple and attractive explanation of the smallness of ν mass Origin of operator

SEESAW MECHANISM

(i) SM+RH ν (EW singlet) (Minkowski 1977)

(ii) SM+SU(2) Triplet Higgs (KonetschnvKummer 1977)

(iii) SM+SU(2) Triplet fermions (RFoot HLew X-G He GC Joshi 1989)

while Ł of the EW int keeps invariant SU(2)timesU(1)

3times3 Seesaw model has 18 parameters 12 real+6 phases (cf Casas Ibarra )

Integrating out the heavy fermions leaves us with observable mass matrix

(9 observables 6 real+3 phases) Half of the parameters of the model get lost at low-E

The 3 low-E CP-violating depend in general on all 6 seesaw phases

The effects of high-E CP-violating phases control the generation of the BAU in the

leptogenesis scenario in |ltmgt| and in the leptonic CP-violating rephasing invariant Jcp

Complicated amp many unknown parameters

2011-11-14

B L

d d

D PMNS RY U m R M

Flavor Symmetry In approaches to reconstruct the high-energy physics from low-energy data

one can assume a flavor symmetry which may reduce the unknown parameters in leading order

For example CKM matrix=Identity+Corrections

PMNS matrix= TBM+Corrections

Unless flavor symmetries are assumed particle masses and mixings are generally

undetermined in gauge theory

A4 S4S3Trsquohelliphellip

Symmetry observed patterns of

Breaking fermion masses and mixings

2011-11-14

Why A4 symmetry To understand the present data we consider A4 flavor symmetry

(EMa and GRajarasekaran GAltarelly and FFeruglio XGHe YYKeum and RVolkas)

Tri-Bimaximal in neutrino mixing amp No Quark mixing

as a good approximation in leading order

Non-zero |Ue3| and correct CKM matrix Higher order corrections

In seesaw + A4

Leptogenesis scale ~ 1013-1015 GeV due to the equal size of moduli of

neutrino Yukawa couplings (strong wash-out)

Without the aid of higher order corrections or soft-breaking term

non-zero |Ue3| as well as Leptogenesis are not possible

TeV-scale Resonant-Leptogenesis

2011-11-14

Why A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

1

3

4

2

A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

A4 Symmetry

Letrsquos denote two A4 triplets and

where

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

So far it is still unclear how to theoretically understand the observed neutrino mixing

A tentative way is to start with the data of ν oscillation and conjecture a simple

constant mixing pattern for example ldquoTri-Bimaximal mixingrdquo matrix

(Harrison Perkins and Scott

see also Wolfenstein(1970) and He and Zee)

It suggests that flavor structure for mixing should be divorced from trying to understand

the mass eigenvalues

Correlations between mass matrix elements It is suggestive of a flavor symmetry

2011-11-14

TBM diag

TBM T12

1

12

2

BM ( )

(

)

(

)

B

A B D

A B

A

m A B Dm

B

D

U U

So far it is still unclear how to theoretically understand the observed neutrino mixing

A tentative way is to start with the data of ν oscillation and conjecture a simple

constant mixing pattern for example ldquoTri-Bimaximal mixingrdquo matrix

(Harrison Perkins and Scott

see also Wolfenstein(1970) and He and Zee)

It suggests that flavor structure for mixing should be divorced from trying to understand

the mass eigenvalues

Correlations between mass matrix elements It is suggestive of a flavor symmetry

2011-11-14

TBM diag

TBM T12

1

12

2

BM ( )

(

)

(

)

B

A B D

A B

A

m A B Dm

B

D

U U

Tri-maximal Θ12=353O

So far it is still unclear how to theoretically understand the observed neutrino mixing

A tentative way is to start with the data of ν oscillation and conjecture a simple

constant mixing pattern for example ldquoTri-Bimaximal mixingrdquo matrix

(Harrison Perkins and Scott

see also Wolfenstein(1970) and He and Zee)

It suggests that flavor structure for mixing should be divorced from trying to understand

the mass eigenvalues

Correlations between mass matrix elements It is suggestive of a flavor symmetry

2011-11-14

TBM diag

TBM T12

1

12

2

BM ( )

(

)

(

)

B

A B D

A B

A

m A B Dm

B

D

U U

So far it is still unclear how to theoretically understand the observed neutrino mixing

A tentative way is to start with the data of ν oscillation and conjecture a simple

constant mixing pattern for example ldquoTri-Bimaximal mixingrdquo matrix

(Harrison Perkins and Scott

see also Wolfenstein(1970) and He and Zee)

It suggests that flavor structure for mixing should be divorced from trying to understand

the mass eigenvalues

Correlations between mass matrix elements It is suggestive of a flavor symmetry

If there exists such a flavor symmetry in Nature the TBM pattern for the neutrino mixing will be a good zeroth order approximation to real world

2011-11-14

TBM diag

TBM T12

1

12

2

BM ( )

(

)

(

)

B

A B D

A B

A

m A B Dm

B

D

U U

Deviations from Tri-Bimaximal It is clear by now that the TBM is not consistent with the recent experimental data

on the reactor mixing angle θ13 because of the vanishing matrix element Ue3 in UTBM

(arXiv 11066028 GLFogli E Lisi A Marrone A Palazzo and AM Rotunno)

Recent data of the T2K Collaboration and the analysis based on global fits of neutrino

oscillations enter into a new phase of precise measurements of the neutrino mixing angles

and mass-squared differences indicating that the TBM mixing for three flavors of leptons

should be modified 2011-11-14

Seesaw A simple and attractive explanation of the smallness of ν mass Origin of operator

SEESAW MECHANISM

(i) SM+RH ν (EW singlet) (Minkowski 1977)

(ii) SM+SU(2) Triplet Higgs (KonetschnvKummer 1977)

(iii) SM+SU(2) Triplet fermions (RFoot HLew X-G He GC Joshi 1989)

while Ł of the EW int keeps invariant SU(2)timesU(1)

3times3 Seesaw model has 18 parameters 12 real+6 phases (cf Casas Ibarra )

Integrating out the heavy fermions leaves us with observable mass matrix

(9 observables 6 real+3 phases) Half of the parameters of the model get lost at low-E

The 3 low-E CP-violating depend in general on all 6 seesaw phases

The effects of high-E CP-violating phases control the generation of the BAU in the

leptogenesis scenario in |ltmgt| and in the leptonic CP-violating rephasing invariant Jcp

Complicated amp many unknown parameters

2011-11-14

B L

d d

D PMNS RY U m R M

Flavor Symmetry In approaches to reconstruct the high-energy physics from low-energy data

one can assume a flavor symmetry which may reduce the unknown parameters in leading order

For example CKM matrix=Identity+Corrections

PMNS matrix= TBM+Corrections

Unless flavor symmetries are assumed particle masses and mixings are generally

undetermined in gauge theory

A4 S4S3Trsquohelliphellip

Symmetry observed patterns of

Breaking fermion masses and mixings

2011-11-14

Why A4 symmetry To understand the present data we consider A4 flavor symmetry

(EMa and GRajarasekaran GAltarelly and FFeruglio XGHe YYKeum and RVolkas)

Tri-Bimaximal in neutrino mixing amp No Quark mixing

as a good approximation in leading order

Non-zero |Ue3| and correct CKM matrix Higher order corrections

In seesaw + A4

Leptogenesis scale ~ 1013-1015 GeV due to the equal size of moduli of

neutrino Yukawa couplings (strong wash-out)

Without the aid of higher order corrections or soft-breaking term

non-zero |Ue3| as well as Leptogenesis are not possible

TeV-scale Resonant-Leptogenesis

2011-11-14

Why A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

1

3

4

2

A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

A4 Symmetry

Letrsquos denote two A4 triplets and

where

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

So far it is still unclear how to theoretically understand the observed neutrino mixing

A tentative way is to start with the data of ν oscillation and conjecture a simple

constant mixing pattern for example ldquoTri-Bimaximal mixingrdquo matrix

(Harrison Perkins and Scott

see also Wolfenstein(1970) and He and Zee)

It suggests that flavor structure for mixing should be divorced from trying to understand

the mass eigenvalues

Correlations between mass matrix elements It is suggestive of a flavor symmetry

2011-11-14

TBM diag

TBM T12

1

12

2

BM ( )

(

)

(

)

B

A B D

A B

A

m A B Dm

B

D

U U

Tri-maximal Θ12=353O

So far it is still unclear how to theoretically understand the observed neutrino mixing

A tentative way is to start with the data of ν oscillation and conjecture a simple

constant mixing pattern for example ldquoTri-Bimaximal mixingrdquo matrix

(Harrison Perkins and Scott

see also Wolfenstein(1970) and He and Zee)

It suggests that flavor structure for mixing should be divorced from trying to understand

the mass eigenvalues

Correlations between mass matrix elements It is suggestive of a flavor symmetry

2011-11-14

TBM diag

TBM T12

1

12

2

BM ( )

(

)

(

)

B

A B D

A B

A

m A B Dm

B

D

U U

So far it is still unclear how to theoretically understand the observed neutrino mixing

A tentative way is to start with the data of ν oscillation and conjecture a simple

constant mixing pattern for example ldquoTri-Bimaximal mixingrdquo matrix

(Harrison Perkins and Scott

see also Wolfenstein(1970) and He and Zee)

It suggests that flavor structure for mixing should be divorced from trying to understand

the mass eigenvalues

Correlations between mass matrix elements It is suggestive of a flavor symmetry

If there exists such a flavor symmetry in Nature the TBM pattern for the neutrino mixing will be a good zeroth order approximation to real world

2011-11-14

TBM diag

TBM T12

1

12

2

BM ( )

(

)

(

)

B

A B D

A B

A

m A B Dm

B

D

U U

Deviations from Tri-Bimaximal It is clear by now that the TBM is not consistent with the recent experimental data

on the reactor mixing angle θ13 because of the vanishing matrix element Ue3 in UTBM

(arXiv 11066028 GLFogli E Lisi A Marrone A Palazzo and AM Rotunno)

Recent data of the T2K Collaboration and the analysis based on global fits of neutrino

oscillations enter into a new phase of precise measurements of the neutrino mixing angles

and mass-squared differences indicating that the TBM mixing for three flavors of leptons

should be modified 2011-11-14

Seesaw A simple and attractive explanation of the smallness of ν mass Origin of operator

SEESAW MECHANISM

(i) SM+RH ν (EW singlet) (Minkowski 1977)

(ii) SM+SU(2) Triplet Higgs (KonetschnvKummer 1977)

(iii) SM+SU(2) Triplet fermions (RFoot HLew X-G He GC Joshi 1989)

while Ł of the EW int keeps invariant SU(2)timesU(1)

3times3 Seesaw model has 18 parameters 12 real+6 phases (cf Casas Ibarra )

Integrating out the heavy fermions leaves us with observable mass matrix

(9 observables 6 real+3 phases) Half of the parameters of the model get lost at low-E

The 3 low-E CP-violating depend in general on all 6 seesaw phases

The effects of high-E CP-violating phases control the generation of the BAU in the

leptogenesis scenario in |ltmgt| and in the leptonic CP-violating rephasing invariant Jcp

Complicated amp many unknown parameters

2011-11-14

B L

d d

D PMNS RY U m R M

Flavor Symmetry In approaches to reconstruct the high-energy physics from low-energy data

one can assume a flavor symmetry which may reduce the unknown parameters in leading order

For example CKM matrix=Identity+Corrections

PMNS matrix= TBM+Corrections

Unless flavor symmetries are assumed particle masses and mixings are generally

undetermined in gauge theory

A4 S4S3Trsquohelliphellip

Symmetry observed patterns of

Breaking fermion masses and mixings

2011-11-14

Why A4 symmetry To understand the present data we consider A4 flavor symmetry

(EMa and GRajarasekaran GAltarelly and FFeruglio XGHe YYKeum and RVolkas)

Tri-Bimaximal in neutrino mixing amp No Quark mixing

as a good approximation in leading order

Non-zero |Ue3| and correct CKM matrix Higher order corrections

In seesaw + A4

Leptogenesis scale ~ 1013-1015 GeV due to the equal size of moduli of

neutrino Yukawa couplings (strong wash-out)

Without the aid of higher order corrections or soft-breaking term

non-zero |Ue3| as well as Leptogenesis are not possible

TeV-scale Resonant-Leptogenesis

2011-11-14

Why A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

1

3

4

2

A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

A4 Symmetry

Letrsquos denote two A4 triplets and

where

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

So far it is still unclear how to theoretically understand the observed neutrino mixing

A tentative way is to start with the data of ν oscillation and conjecture a simple

constant mixing pattern for example ldquoTri-Bimaximal mixingrdquo matrix

(Harrison Perkins and Scott

see also Wolfenstein(1970) and He and Zee)

It suggests that flavor structure for mixing should be divorced from trying to understand

the mass eigenvalues

Correlations between mass matrix elements It is suggestive of a flavor symmetry

2011-11-14

TBM diag

TBM T12

1

12

2

BM ( )

(

)

(

)

B

A B D

A B

A

m A B Dm

B

D

U U

So far it is still unclear how to theoretically understand the observed neutrino mixing

A tentative way is to start with the data of ν oscillation and conjecture a simple

constant mixing pattern for example ldquoTri-Bimaximal mixingrdquo matrix

(Harrison Perkins and Scott

see also Wolfenstein(1970) and He and Zee)

It suggests that flavor structure for mixing should be divorced from trying to understand

the mass eigenvalues

Correlations between mass matrix elements It is suggestive of a flavor symmetry

If there exists such a flavor symmetry in Nature the TBM pattern for the neutrino mixing will be a good zeroth order approximation to real world

2011-11-14

TBM diag

TBM T12

1

12

2

BM ( )

(

)

(

)

B

A B D

A B

A

m A B Dm

B

D

U U

Deviations from Tri-Bimaximal It is clear by now that the TBM is not consistent with the recent experimental data

on the reactor mixing angle θ13 because of the vanishing matrix element Ue3 in UTBM

(arXiv 11066028 GLFogli E Lisi A Marrone A Palazzo and AM Rotunno)

Recent data of the T2K Collaboration and the analysis based on global fits of neutrino

oscillations enter into a new phase of precise measurements of the neutrino mixing angles

and mass-squared differences indicating that the TBM mixing for three flavors of leptons

should be modified 2011-11-14

Seesaw A simple and attractive explanation of the smallness of ν mass Origin of operator

SEESAW MECHANISM

(i) SM+RH ν (EW singlet) (Minkowski 1977)

(ii) SM+SU(2) Triplet Higgs (KonetschnvKummer 1977)

(iii) SM+SU(2) Triplet fermions (RFoot HLew X-G He GC Joshi 1989)

while Ł of the EW int keeps invariant SU(2)timesU(1)

3times3 Seesaw model has 18 parameters 12 real+6 phases (cf Casas Ibarra )

Integrating out the heavy fermions leaves us with observable mass matrix

(9 observables 6 real+3 phases) Half of the parameters of the model get lost at low-E

The 3 low-E CP-violating depend in general on all 6 seesaw phases

The effects of high-E CP-violating phases control the generation of the BAU in the

leptogenesis scenario in |ltmgt| and in the leptonic CP-violating rephasing invariant Jcp

Complicated amp many unknown parameters

2011-11-14

B L

d d

D PMNS RY U m R M

Flavor Symmetry In approaches to reconstruct the high-energy physics from low-energy data

one can assume a flavor symmetry which may reduce the unknown parameters in leading order

For example CKM matrix=Identity+Corrections

PMNS matrix= TBM+Corrections

Unless flavor symmetries are assumed particle masses and mixings are generally

undetermined in gauge theory

A4 S4S3Trsquohelliphellip

Symmetry observed patterns of

Breaking fermion masses and mixings

2011-11-14

Why A4 symmetry To understand the present data we consider A4 flavor symmetry

(EMa and GRajarasekaran GAltarelly and FFeruglio XGHe YYKeum and RVolkas)

Tri-Bimaximal in neutrino mixing amp No Quark mixing

as a good approximation in leading order

Non-zero |Ue3| and correct CKM matrix Higher order corrections

In seesaw + A4

Leptogenesis scale ~ 1013-1015 GeV due to the equal size of moduli of

neutrino Yukawa couplings (strong wash-out)

Without the aid of higher order corrections or soft-breaking term

non-zero |Ue3| as well as Leptogenesis are not possible

TeV-scale Resonant-Leptogenesis

2011-11-14

Why A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

1

3

4

2

A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

A4 Symmetry

Letrsquos denote two A4 triplets and

where

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

So far it is still unclear how to theoretically understand the observed neutrino mixing

A tentative way is to start with the data of ν oscillation and conjecture a simple

constant mixing pattern for example ldquoTri-Bimaximal mixingrdquo matrix

(Harrison Perkins and Scott

see also Wolfenstein(1970) and He and Zee)

It suggests that flavor structure for mixing should be divorced from trying to understand

the mass eigenvalues

Correlations between mass matrix elements It is suggestive of a flavor symmetry

If there exists such a flavor symmetry in Nature the TBM pattern for the neutrino mixing will be a good zeroth order approximation to real world

2011-11-14

TBM diag

TBM T12

1

12

2

BM ( )

(

)

(

)

B

A B D

A B

A

m A B Dm

B

D

U U

Deviations from Tri-Bimaximal It is clear by now that the TBM is not consistent with the recent experimental data

on the reactor mixing angle θ13 because of the vanishing matrix element Ue3 in UTBM

(arXiv 11066028 GLFogli E Lisi A Marrone A Palazzo and AM Rotunno)

Recent data of the T2K Collaboration and the analysis based on global fits of neutrino

oscillations enter into a new phase of precise measurements of the neutrino mixing angles

and mass-squared differences indicating that the TBM mixing for three flavors of leptons

should be modified 2011-11-14

Seesaw A simple and attractive explanation of the smallness of ν mass Origin of operator

SEESAW MECHANISM

(i) SM+RH ν (EW singlet) (Minkowski 1977)

(ii) SM+SU(2) Triplet Higgs (KonetschnvKummer 1977)

(iii) SM+SU(2) Triplet fermions (RFoot HLew X-G He GC Joshi 1989)

while Ł of the EW int keeps invariant SU(2)timesU(1)

3times3 Seesaw model has 18 parameters 12 real+6 phases (cf Casas Ibarra )

Integrating out the heavy fermions leaves us with observable mass matrix

(9 observables 6 real+3 phases) Half of the parameters of the model get lost at low-E

The 3 low-E CP-violating depend in general on all 6 seesaw phases

The effects of high-E CP-violating phases control the generation of the BAU in the

leptogenesis scenario in |ltmgt| and in the leptonic CP-violating rephasing invariant Jcp

Complicated amp many unknown parameters

2011-11-14

B L

d d

D PMNS RY U m R M

Flavor Symmetry In approaches to reconstruct the high-energy physics from low-energy data

one can assume a flavor symmetry which may reduce the unknown parameters in leading order

For example CKM matrix=Identity+Corrections

PMNS matrix= TBM+Corrections

Unless flavor symmetries are assumed particle masses and mixings are generally

undetermined in gauge theory

A4 S4S3Trsquohelliphellip

Symmetry observed patterns of

Breaking fermion masses and mixings

2011-11-14

Why A4 symmetry To understand the present data we consider A4 flavor symmetry

(EMa and GRajarasekaran GAltarelly and FFeruglio XGHe YYKeum and RVolkas)

Tri-Bimaximal in neutrino mixing amp No Quark mixing

as a good approximation in leading order

Non-zero |Ue3| and correct CKM matrix Higher order corrections

In seesaw + A4

Leptogenesis scale ~ 1013-1015 GeV due to the equal size of moduli of

neutrino Yukawa couplings (strong wash-out)

Without the aid of higher order corrections or soft-breaking term

non-zero |Ue3| as well as Leptogenesis are not possible

TeV-scale Resonant-Leptogenesis

2011-11-14

Why A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

1

3

4

2

A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

A4 Symmetry

Letrsquos denote two A4 triplets and

where

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Deviations from Tri-Bimaximal It is clear by now that the TBM is not consistent with the recent experimental data

on the reactor mixing angle θ13 because of the vanishing matrix element Ue3 in UTBM

(arXiv 11066028 GLFogli E Lisi A Marrone A Palazzo and AM Rotunno)

Recent data of the T2K Collaboration and the analysis based on global fits of neutrino

oscillations enter into a new phase of precise measurements of the neutrino mixing angles

and mass-squared differences indicating that the TBM mixing for three flavors of leptons

should be modified 2011-11-14

Seesaw A simple and attractive explanation of the smallness of ν mass Origin of operator

SEESAW MECHANISM

(i) SM+RH ν (EW singlet) (Minkowski 1977)

(ii) SM+SU(2) Triplet Higgs (KonetschnvKummer 1977)

(iii) SM+SU(2) Triplet fermions (RFoot HLew X-G He GC Joshi 1989)

while Ł of the EW int keeps invariant SU(2)timesU(1)

3times3 Seesaw model has 18 parameters 12 real+6 phases (cf Casas Ibarra )

Integrating out the heavy fermions leaves us with observable mass matrix

(9 observables 6 real+3 phases) Half of the parameters of the model get lost at low-E

The 3 low-E CP-violating depend in general on all 6 seesaw phases

The effects of high-E CP-violating phases control the generation of the BAU in the

leptogenesis scenario in |ltmgt| and in the leptonic CP-violating rephasing invariant Jcp

Complicated amp many unknown parameters

2011-11-14

B L

d d

D PMNS RY U m R M

Flavor Symmetry In approaches to reconstruct the high-energy physics from low-energy data

one can assume a flavor symmetry which may reduce the unknown parameters in leading order

For example CKM matrix=Identity+Corrections

PMNS matrix= TBM+Corrections

Unless flavor symmetries are assumed particle masses and mixings are generally

undetermined in gauge theory

A4 S4S3Trsquohelliphellip

Symmetry observed patterns of

Breaking fermion masses and mixings

2011-11-14

Why A4 symmetry To understand the present data we consider A4 flavor symmetry

(EMa and GRajarasekaran GAltarelly and FFeruglio XGHe YYKeum and RVolkas)

Tri-Bimaximal in neutrino mixing amp No Quark mixing

as a good approximation in leading order

Non-zero |Ue3| and correct CKM matrix Higher order corrections

In seesaw + A4

Leptogenesis scale ~ 1013-1015 GeV due to the equal size of moduli of

neutrino Yukawa couplings (strong wash-out)

Without the aid of higher order corrections or soft-breaking term

non-zero |Ue3| as well as Leptogenesis are not possible

TeV-scale Resonant-Leptogenesis

2011-11-14

Why A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

1

3

4

2

A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

A4 Symmetry

Letrsquos denote two A4 triplets and

where

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Seesaw A simple and attractive explanation of the smallness of ν mass Origin of operator

SEESAW MECHANISM

(i) SM+RH ν (EW singlet) (Minkowski 1977)

(ii) SM+SU(2) Triplet Higgs (KonetschnvKummer 1977)

(iii) SM+SU(2) Triplet fermions (RFoot HLew X-G He GC Joshi 1989)

while Ł of the EW int keeps invariant SU(2)timesU(1)

3times3 Seesaw model has 18 parameters 12 real+6 phases (cf Casas Ibarra )

Integrating out the heavy fermions leaves us with observable mass matrix

(9 observables 6 real+3 phases) Half of the parameters of the model get lost at low-E

The 3 low-E CP-violating depend in general on all 6 seesaw phases

The effects of high-E CP-violating phases control the generation of the BAU in the

leptogenesis scenario in |ltmgt| and in the leptonic CP-violating rephasing invariant Jcp

Complicated amp many unknown parameters

2011-11-14

B L

d d

D PMNS RY U m R M

Flavor Symmetry In approaches to reconstruct the high-energy physics from low-energy data

one can assume a flavor symmetry which may reduce the unknown parameters in leading order

For example CKM matrix=Identity+Corrections

PMNS matrix= TBM+Corrections

Unless flavor symmetries are assumed particle masses and mixings are generally

undetermined in gauge theory

A4 S4S3Trsquohelliphellip

Symmetry observed patterns of

Breaking fermion masses and mixings

2011-11-14

Why A4 symmetry To understand the present data we consider A4 flavor symmetry

(EMa and GRajarasekaran GAltarelly and FFeruglio XGHe YYKeum and RVolkas)

Tri-Bimaximal in neutrino mixing amp No Quark mixing

as a good approximation in leading order

Non-zero |Ue3| and correct CKM matrix Higher order corrections

In seesaw + A4

Leptogenesis scale ~ 1013-1015 GeV due to the equal size of moduli of

neutrino Yukawa couplings (strong wash-out)

Without the aid of higher order corrections or soft-breaking term

non-zero |Ue3| as well as Leptogenesis are not possible

TeV-scale Resonant-Leptogenesis

2011-11-14

Why A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

1

3

4

2

A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

A4 Symmetry

Letrsquos denote two A4 triplets and

where

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Flavor Symmetry In approaches to reconstruct the high-energy physics from low-energy data

one can assume a flavor symmetry which may reduce the unknown parameters in leading order

For example CKM matrix=Identity+Corrections

PMNS matrix= TBM+Corrections

Unless flavor symmetries are assumed particle masses and mixings are generally

undetermined in gauge theory

A4 S4S3Trsquohelliphellip

Symmetry observed patterns of

Breaking fermion masses and mixings

2011-11-14

Why A4 symmetry To understand the present data we consider A4 flavor symmetry

(EMa and GRajarasekaran GAltarelly and FFeruglio XGHe YYKeum and RVolkas)

Tri-Bimaximal in neutrino mixing amp No Quark mixing

as a good approximation in leading order

Non-zero |Ue3| and correct CKM matrix Higher order corrections

In seesaw + A4

Leptogenesis scale ~ 1013-1015 GeV due to the equal size of moduli of

neutrino Yukawa couplings (strong wash-out)

Without the aid of higher order corrections or soft-breaking term

non-zero |Ue3| as well as Leptogenesis are not possible

TeV-scale Resonant-Leptogenesis

2011-11-14

Why A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

1

3

4

2

A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

A4 Symmetry

Letrsquos denote two A4 triplets and

where

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Why A4 symmetry To understand the present data we consider A4 flavor symmetry

(EMa and GRajarasekaran GAltarelly and FFeruglio XGHe YYKeum and RVolkas)

Tri-Bimaximal in neutrino mixing amp No Quark mixing

as a good approximation in leading order

Non-zero |Ue3| and correct CKM matrix Higher order corrections

In seesaw + A4

Leptogenesis scale ~ 1013-1015 GeV due to the equal size of moduli of

neutrino Yukawa couplings (strong wash-out)

Without the aid of higher order corrections or soft-breaking term

non-zero |Ue3| as well as Leptogenesis are not possible

TeV-scale Resonant-Leptogenesis

2011-11-14

Why A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

1

3

4

2

A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

A4 Symmetry

Letrsquos denote two A4 triplets and

where

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Why A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

1

3

4

2

A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

A4 Symmetry

Letrsquos denote two A4 triplets and

where

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

1

3

4

2

A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

A4 Symmetry

Letrsquos denote two A4 triplets and

where

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

A4 Symmetry A4 is the symmetry group of the tetrahedron and the finite groups of the even

permutation of four objects its irreducible representations contain one triplet 3 and three singlets 11rsquo1rdquo with the multiplication rules 3times3=3+3+1+1rsquo+1rdquo and 1rsquotimes1rsquo=1rdquo The 12 representation matrices for 3 Identity matrix I matrices r1=diag(1-1-1) r2=diag(-11-1) r3=diag(-1-11) matrices

1 1

0 0 1 0 1 0

1 0 0 0 0 1

0 1 0 1 0 0

i i i ic a a c rcr rar

2011-11-14

A4 Symmetry

Letrsquos denote two A4 triplets and

where

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

A4 Symmetry

Letrsquos denote two A4 triplets and

where

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Construction of Lagrangian Under SU(2)timesU(1)timesA4timesZ2

Hence its Yukawa interaction

Z2 forbidden

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Can we obtain the required VEV alignment If the flavor symmetry associated to A4 is broken by the VEV of a triplet Φ and χ of scalar

fields there are two interesting breaking pattern

ltΦgt=(111) A4Z3 ltχgt=(100) A4Z2

Under SU(2)timesU(1)timesA4timesZ2 the most general renormalizable scalar potential of Φη and χ

(NPB 72064

Problematic interaction term V(Φχ ) GAltarelli

FFeruglio)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

In the charged fermion sector

Assumption the VEVs of A4 triplets can be equally aligned ie

ldquoTri-maximalrdquo

Lepton-sector

Charged fermion mass matrix comes from and has the form U(w)times Diag(arbitrary eigenvalues)

Quark sector In a weak eigenstate basis

When diagonalizing the charged fermion mass matrices

by rotating

No Mixing it should be corrected

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

In the neutrino sector

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

No Leptogenesis and No low-E CP-violation

Taking the scale of A4 symmetry breaking to be above EW scale

Heavy Majorana

mass matrix

And assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

In the neutrino sector

If we consider

Leptogenesis and low-energy CP-violation in our scenario

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction Lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

Neutrino

mass matrix

as which leads to an effective neutrino mass matrix at low energies

Diagonalizing matrix of light neutrino mass matrix is

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

In a weak eigenstate basis the Yukawa interaction and charged gauge interaction lagrangian

By rotating

From the charged lepton current

Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector)

Non-zero |Ue3|

QLC

Leptogenesis

Consider Naiumlve and very simple corrections to the Quarks and lepton sectors

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Deviations TBM from higher dimensional operators In the Lagrangian level assume that above the cutoff scaleΛ there is no CP violation term in the

Dirac Yukawa neutrino and charged fermion Yukawa interactions which for scale below Λ is

expressed in terms of 5-dimentional operators

In the presence of 5-D operators driven byχ -VEV alignment the Yukawa interactions

in the fermion sector which is invariant under SU(2)timesU(1)timesA4timesZ2

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

In the neutrino sector

Taking the scale of A4 symmetry breaking to be above EW scale

and assuming the vacuum alignment of heavy singlet scalar

where

The Yukawa interaction after EW symmetry breaking Z2 symmetry breaking

The corrected

neutrino Yukawa matrix

Leptogenesis low-E CP violation

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

In the charged fermion sector VEV alignment

The corrected charged

fermion mass matrix

Only the mixing matrix takes part in PMNS and CKM mixing matrices

Low-energy CP-violation

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

For the most natural case of hierarchical charged fermion Yukawa couplings

the corrected off-diagonal terms are not larger than the diagonal ones in size

There are empirical fermion mass ratios in the charged-lepton up- and down-type

quark sectors calculated from the measured values (PDG)

mumcmt=λ8λ41 mdmsmb=λ4λ21 memμmτ=λ5λ21

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Quark-Lepton symmetry is broken by masses of quarks and lepton

therefore one does not expect that the quark mixing is transmitted to

the lepton sector exactly

However there is some interesting empirical relation

The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type

onersquos on the other hand the mass spectrum of up-type quark shows a strong hierarchy

compared to the down-type onersquos

In terms of the Cabbibo angle the fermion masses can be scaled as

which may represent that the CKM matrix mainly generated from the down-type-quark

sector as well as charged-lepton mixing matrix is similar to the CKM matrix

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

CKM Mixing Matrix Up-type quark and its mixing matrix

Due to the measured up-quark mass hierarchy it is not possible to generate the

Cabbibo angle

if let then

which is in discrepancy with the measured

does not affect the leading order predictions in λ

Cabbibo angle should arise from the first and second generation mixing

in the down-type quark sector

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

CKM Mixing Matrix Down-type quark and its mixing matrix From the measured down-quark mass hierarchies

For letting

in turn which means should be roughly

Assumption to get a correct CKM matrix

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein A λ ρη

Qin-Ma f h λ δQM

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

CKM Mixing Matrix If the CKM comes from down-type quark sector after redefinition of quark fields

3 (mixing angles)+6 (phases) 3 (mixing angles)+1 (phase) 4 parameters

CKM mixing matrix

Wolfenstein

Qin-Ma

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Charged-Lepton sector From the measured charged-lepton mass hierarchies

Similar to down-type quark sector if let

which means

Scenario-I

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Charged-Lepton sector Scenario-II

Similar to Down-type quark mixing matrix

Scenario-III

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Charged-Lepton sector In a mass eigenstate basis of the charged gauge interaction term

Charged-lepton sector Neutrino sector

3 mixing angles + 6 phases Pf can be rotated away by redefinitions of

charged-fermion fields 3 mixing angle+3 phases

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Neutrino sector The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing

An additional mixing matrix to diagonalize

with the mixing angle and phases

2011-11-14

θ=plusmn π4 +δ for δlaquo 1

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Neutrino sector The neutrino mass eigenvalues are given as

From the above the solar and atmospheric mass squared differences are written as

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

PMNS Mixing (charged lepton correction)

where

Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are

sensitive to the Dirac-phase but insensitive to the Majorana phases

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

PMNS Mixing (charged lepton correction) Solar mixing angle

For example in the second scenario

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

PMNS Mixing (charged lepton correction) Reactor mixing angle

The parameter

can be determined by the BAU

if Leptogenesis is true

Subsequently the parameter Φ(φ21θψ3)

can be decided by the first QLC relation

And then we can predict the value of reactor angle

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

PMNS Mixing (charged lepton correction) Atmospheric mixing angle

where

If we consider Leptogenesis in this scenario

then we can pin down the value of ψ1

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

θ12+θq12 =45ο θ23+θq23 =45ο

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

PMNS Mixing (charged lepton correction) Solar Mixing Angle versus ψ3 Atm Mixing Angle versus ψ1

ψ2 does not affect crucially

+O(λ4)

PLB 695194(QIN-MA) ARXIV 11074549 (AHN-CHENG-OH)

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

PMNS Mixing (charged lepton correction) Non-zero |Ue3| Leptonic CP-violation JCP

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Another very attractive feature of Seesaw In addition to the explanation of neutrino masses seesaw has another appearing feature so-called

ldquoLeptogenesisrdquo

Lepton asymmetry

It is independent of mixing angles and CP phases of neutrino oscillation

The loop function includes the 1-loop vertex and self energy corrections to the heavy

neutrino decay amplitude

i

i

NB L BB

N L

nn n ns s

s n s n n n

( ) ( )

MATTER antimatter

i iBr N Br N

0

i

i i

N

n n

n

( ) 1 (1 ) ln1 1

x xf x x x

x x

2011-11-14

dagger 2

dagger 2

Im( ) ( ) ( )

8 ( )

ij i j j

i

j i ii i

Y Y Y Y Mf

Y Y M

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Another very attractive feature of Seesaw wash-out effects

The generated asymmetry survives if decays takes place out-of-equilbrium at

otherwise inverse decay and scattering processes cancel the asymmetry

We are in the energy scale where A4 symmetry is broken but the SM gauge group remains

unbroken Choose leptogenesis scale

Flavor effects (PRD496394

James M Cline Kimmo Kainulainen Keith A Olive)

Interactions involving the charged τ are out-of-equilibrium at

Interactions involving the charged μ are out-of-equilibrium at

Interactions involving the charged e are out-of-equilibrium at

23 2

EQ

Pl

5 10 for T

y T H T TM

iT M

2011-11-14

1210 GeV ( )T H 910 GeV ( )T H

510 GeV ( )eT H

iN e e

iB B

i

L

ii i

nn n

s s n

iN eB Bi i

e

i i ii

L

nn n

s s n

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

A link between low-energy observables and Leptogenesis Go into the physical basis of the RH neutrino

Diagonalizing matrix

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14

Conclusions

In the presence of 5-Dimensional operators driven by χ-field

A relatively large |Ue3| and CKM mixing matrix can be explained

QLC can be naturally explained in A4 flavor symmetry through phased-effects

The deviations from TBM can be fitted to Experimental data especially a relatively

large Theta13 through the phased effects from higher dimensional operators

Quark-lepton unification in parametrization

If we consider the BAU through Leptogenesis in this scenario

we can have more informations and give predictions about neutrino data

2011-11-14