Quark-Lepton Complementarityin light of recent T2K & MINOS experi-

ments

November 18, 2011 Yonsei University

Sin Kyu Kang (서울과학기술대학교 )

Outline• Introduction - current status of neutrino mixing angles• Parameterizations of neutrino mixing matrix• Quark mixing angles and Quark-Lepton

Complementarity (QLC)• QLC parameterizations and Triminimal

parametrization• Predictions of physical observables• Summary

Purposes of this work • To investigate whether neutrino mixing matrix

based on Quark-Lepton Complementarity (QLC) reflecting GUT relations or quark-lepton symmetry is consistent with current neutrino data or not.

• To investigate how we can achieve large values of mixing angle q13 so as to accommodate recent T2K or MINOS experimental results.

• To point out that nonzero values of q13 can be re-lated to the deviation of q12 from maximal mixing or tri-bimaximal mixing

Neutrino Mixing Matrixe

Le

L

L

Atmo-spheric angle

Reactor angle and Dirac CP phase

Solar angle Majorana phases

Standard Model states

Neutrino mass states

3

2

1

321

321

321

UUUUUUUUU eeee

1000000

10000

0010

0

00

0012

1

1212

1212

1313

1313

2323

2323

i

i

i

i

ee

cssc

ces

esc

csscU

CP

CP

Neutrino mixing anlges before T2K( Schwetz, Tortola, Valle, New J.Phys.13:063004,2011. )

)(2 10.2 , 51.439.9 , 4.369.31

75.5 , 6.45 , 9.33

132312

132312

qqq

qqq

Neutrino data for neutrino mixing angles is consistent with “Tri-bimaximal mixing” pattern at 2σ

21

31

61

21

31

61

03

16

2

U

0 , 45 , 3.35 132312 qqq

3

13

13

12 e

2

12

13

It can be derived from some discrete symmet-ries such as A4, S4 etc.

Recent T2K experimentThe results show

(CPC) eV 102.4|m|

0.12sinfor

C.L. 90%at )34.0(28.02sin)04.0(03.0

23-223

232

132

q

q

For non-maximal 23 mix-ing

132

232

132 2cossin22sin qqq

More data needed to firmly establish νe appearance and to better deter-mine θ13

155 13 q

Recent MINOS experiment( 1.7 excess of e events )

0.6 , 100 1313 bestqq 5.8 , 130 1313 bestqq

Although TB mixing can be achieved by imposing some flavor symmetries, the current neutrino data indicates that TB is a good zeroth order approxima-tion to reality and there may be deviations from TB in general. To accommodate deviations from TB, neutrino mixing angles can be parameterized (S.F.King 2008)

2sin , )1(

21sin , )1(

31sin 132312

ras qqq

The global fit of the neutrino mixing angles can be translated into the 3σ

0.14 a 0.18- , 0.03 s 0.10- , 31.00 r

Alternatively, triminimal parametrization has been proposed

)()()(

300121-012

611-0110002

31sin),,,(

4

212113132323

11221132323

RURURU

U

RURUTMin

(Pakvasa, Rodejohann, Weiler, Phys. Rev. Lett.100 ,2008 )

The neutrino mixing observables up to 2nd order in

qq

ie eU

133

323222

2121212

sin 21sin ,

31

322

31sin

ij

Quark Mixing Angles

Current data for quark mixing angles0.9739 0.9751 0.221 0.227 0.0029 0.00450.221 0.227 0.9730 0.9744 0.039 0.044

0.0048 0.014 0.037 0.043 0.9990 0.9992

The standard parameterization of VCKM

quark-s and -d of Rotation

rphasefacto plusquark-b and -d of Rotationquark-b and -s of Rotation

10000

0010

0

00

001

1212

1212

1313

1313

2323

2323, cssc

ces

esc

csscV

i

i

SCKM

SCKMV ,

Wolfenstein Parameterization of quark mixing matrix

0.82,A

2 3

2 2

3 2

11 ( )2

112

(1 ) 1

A i

V A

A i A

0.2243 0.0016, 0.20, 0.33.

L. Wolfenstein, Phys. Rev. Lett. 51 (1983)

Quark Lepton ComplimentarityLepton mix-ings

Quark mix-ings

Present experimental data allows for relations like:

Raidal (2004) Smirnov, Minakata (2004)

'Quark-Lepton Complementarity‘

45

45

2323

12

q

C

qq

qq

QLC is well in consistent with the current data within 2σ

QLC may serve as a clue to quark-lepton symmetry or unification. So, QLC motivates measurements of neutrino mixing angles to at least the accuracy of the meas-ured quark mixing angles. In the light of QLC, neutrino mixing matrix can be composed of CKM mixing matrix and maximal mixing matrix. Three possible combinations of maximal mixing and CKM as parametrization of neutrino mixing matrix (Cheung, Kang, Kim, Lee (2005), Datta, Everett, Ramond (2005) )

)4()4( )3(

)4()4( )2(

)4()4( )1(

1223

1223

1223

RUR

URR

RRU

CKM

CKM

CKM

Among three possible combinations, 4)4( 1223max RRVVVU CKMbiCKMPMNS

2 ,

4 ,

24 132 qqq Aatmsol

Mixing angles in powers of λ

9 , 43 , 36 1323 qqq sol

consistent with the current experimental data.

Among three possible combinations, 4 )4(23 RVRU CKMPMNS

313

2 ,4

,4

qqq AAatmsol

Mixing angles in powers of λ

5.0 , 43 , 33 1323 qqq sol

consistent with the current experimental data, but disfavored by T2K measurement of q13

Among three possible combinations, CKMPMNS VRRU 4)4( 1223

213

2 ,4

,24

qqq AAatmsol

Mixing angles in powers of λ

2 , 43 , 36 1323 qqq sol

consistent with the current experimental data , but disfavored by only T2K measurement of q13 at 90%CL.

The flavor mixings stem from the mismatch be-tween the LH rotations of the up-type and down-type quarks, and the charged leptons and neutri-nos.

In general, the quark Yukawa matrices

DdiagDDD

UdiagUUU

VYUY

VYUY

DUCKM UUV

For charged lepton sector : LdiagLLL VYUY

How to derive those parameterizations

For neutrino sector : Introducing one RH singlet neutrino per family which leads to the seesaw mechanism

Rewriting neutrino mass,

MLPMNS VUUU 0

In SO(10), TDLU YYYY ,

Taking symmetric YD , MCKMPMNS VVU

UDL UUVU 0* ,

Taking )4(23 RUV DTD MCKMPMNS VVRU )4(23

Taking maxbiD

TD VUV CKMPMNS VRRU /4)()4( 1223

Realistic neutrino mixing matrix,

4)4()( 1223 RRVUPMNS

We need to modify

5.3 , 43 , 41 1323 qqq sol

Then, neutrino mixing angles becomes

From the empirical relation, m

mmmV e

S

dUS 3

)(12

213331

~ 2

2

qq

qq

VVCKM

In GUT framework,

At low energies, the Yukawa operators of the SM (MSSM) are generated from integrating out heavy fields X which lead to GUT relations be-tween q and l

In SU(5) GUT,

4)4()( 1223 RRVUPMNS

6 , 43 , 39 1323 qqq sol

Then, neutrino mixing angles becomes

232 ,

4 ,

232

4 132 qqq atmsol

In Pati-Salam GUT (Antusch & Sinrath (2009) ),

2 ,

4 ,

24 2

113

2

2

1

cc

cc

atmsolqqq

it is possible to have 6 , 2/9 21 cc

8 , 43 , 36 1323 qqq sol

What if replacing R12(/4) with tri-bimaximal type ?

))3/1((sin)4( 11223

RRUCKM

))3/1((sin)4/( 11212

RR

QLC parameterizations become

For realistic GUT relation, we replace UCKM U()

23 ,

4 ,

36 132max qqqq

atmbitri

solsol

It is possible to obtain rather large q13 while keeping small deviation of q12

Lepton Flavor Violation in the SUSY caused by the misalignment of lepton and slepton mass matrices

RG inducesX

ijl MM

YYAmmij

log))(3(81 2

020

2~

)4()()4( 232

23 RUYURYY CKM

DCKM

]1,,[ 48 DiagyY tD Taking

1::)(:)(:)( 66 BReBReBR

(cf)

1::)(:)(:)()4()4(

1::)(:)(:)()4()4(44

1223

481223

BReBReBRURR

BReBReBRRRU

CKM

CKM

4)4( 1223 RRVU CKMPMNS

Predictions for Physical Observables Neutrino mixing probabilities for phased averaged propa-gation(Δm2L/4E >>1) iiii UUUUP

|||| 22

AAS 22

(Pakvasa, Rodejohann, Weiler, Phys. Rev. Lett.100 ,2008 )

Using the previous formulae, we obtain

, )1(21

83 ,)

211(

41

, 21

83 ,)

211(

41

, )1(21

83 ,2

21

22

22

22

APAP

PAP

APP

e

e

ee

Using the best fit values for the parameters

, 421.0 ,401.0

, 380.0 ,178.0

, 220.0 ,602.0

PP

PP

PP

e

e

ee

The phase-averaged mixing matrix modi-fies the flavor composition of the neutrino fluxes.

iU

The most common source for atmospheric and astrophysical neutrinos is thought to be pion production and decay. The pion decay chain generates an initial neutrino flux with a flavor composition given approximately for the neutrino fluxes :

(P. Lipari, M. Lusignoli, and D. Meloni (2007))

0:2:1:: 000 e

At the Earth :

1:1 : 1.2

)5.01(:)5.01(:)41(:: 222

AAAe

Matching with triminimal parametrization

6/)12(6/)12(s 1sin

sin

)1(sin

22

2

12

23232

31313

ccs

cscs

A

iAee ii

31sin),,,()4(

4 )4(1

1212132323

1223

RUR

RVRU CKMPMNS

In the light of recent data from T2K,

Final Remark

)4()4( 1223 RRUCKM

more favorable because it predicts

2sin 13

q

Summary• We have discussed that neutrino mixing matrix based on

Quark-Lepton Complementarity (QLC) reflecting GUT rela-tions or quark-lepton symmetry is consistent with global fit to current neutrino data at 2 but some of QLC param-eterizations disfavored by T2K

• We have shown how we can achieve large values of mix-ing angle q13 so as to accommodate recent T2K or MINOS experimental results.

• We have observed that QLC based on GUT relations lead to the relation between nonzero values of q13 and the de-viation of q12 from maximal mixing or tri-bimaximal mixing