the νmsm - 東京大学the νmsm takehiko asaka (niigata university) @ icrr, tokyo univ. 02 nov....
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Neutrino masses, dark matter and baryon asymmetry
The νMSM
Takehiko Asaka(Niigata University)
@ ICRR, Tokyo Univ. 02 Nov. 2007
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Prologue: Physics beyond the MSMAbout 10 years ago …,
There was no “convincing” evidence for physics beyond the minimal standard model (MSM)
People looked for physics beyond the MSM “mainly”based on theoretical arguments:
• Hierarchy problem• Gravity, String, …• Strong CP problem• Why 3 generations?• Why anomalies cancel?• …
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Neutrino Oscillations
Cosmic MicrowaveBackground (CMB)
[SuperK]
[WMAP]
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Physics beyond the MSMIn the last decade(s), we have collected quite “convincing” evidences for physics beyond the MSM
Neutrino oscillations non-zero neutrino masses
Baryon asymmetry
Dark matter
Dark energy
Scale-invariant density perturbations
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Physics beyond the MSMIn the last decade(s), we have collected quite “convincing” evidences for physics beyond the MSM
Neutrino oscillations non-zero neutrino masses
Baryon asymmetry
Dark matter
Dark energy
Scale-invariant density perturbations
Today, I would like to explain the νMSM, which can solve first three problems!
????
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The νMSM= the “neutrino” Minimal Standard Model
Dark matter in the νMSM
Baryogenesis in the νMSM
Summary
Outline
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Neutrino oscillationsEvidence of neutrino oscillations
non-zero neutrino masses
Atmospheric• Atmospheric neutrino exps. (…, SuperK)• Long-baseline accelerator exps. (K2K, MINOS)
Solar• Solar neutrino exps. (…, SuperK, SNO)• Reactor exp. (KamLand)
Need for physics beyond the minimal standard model (MSM)
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The νMSMAdding three right-handed neutrinos NI (I=1,2,3)
18 new parameters• 3 Majorana masses• 15 parameters in Yukawa coupling matrix
– 3 Yukawa couplings– 6 mixing angles – 6 phases
Dirac and Majorana masses of neutrinos
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Seesaw mechanismIf Majorana masses >> Dirac masses,
active neutrinos
sterile neutrinos
Mixing in CC current
0 0
0D
TD M M
MM
MM M
ν⎛ ⎞ ⎛ ⎞⇒⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠
1TD D
M
M M MMν = −
acIa IU Nα α αν θν= +
( ) / 1I D I IM Mα αθ =
1 2 3 1 2 3, , ( )m m mν ν ν ≤ ≤
1 2 3 1 2 3, , ( )N N N M M M≤ ≤
1 2 3( , , )TU M U diag m m mν =
1 2 3( , , )MM diag M M M=
( , , )eα μ τ= ( 1,2,3)a =
active-sterile mixing
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Scale for Majorana massNeutrino oscillations are explained by flavor mixing between active neutrinos !
Masses of active neutrinos
Where is the scale of Majorana mass ??Two “natural” options• Conventional seesaw• The νMSM
1TD D
M
M M MMν = −
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Convenstional seesaw scenario:Neutrino Yukawa couplings are comparable to those of quarks and charged leptons
MR >> 100GeV
• Explain smallness of neutrino masses via seesaw
• Decays of RH neutrino(s) can account for baryon asymmetry through leptogenesis
• Physics of RH neutrino cannot be tested directly by experiments
[Fukugita, Yanagida]
[Yanagida; Gell-Mann, Ramond, Slansky]
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The νMSM:No new mass scale is introduced
MR ~<100GeV
• Lightest RH neutrino (~keV) can be DM (?)
• Oscillation of RH neutrinos can account for baryon asymmetry of the universe
• Physics of RH neutrinos can potentially tested by experiments
[TA, Blanchet, Shaposhnikov; TA, Shposhnikov]
[Dodelson, Widrow,…]
[Akhmedov, Rubakov, Smirnov]
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Scale of Majorana mass
1 TD D
M
M M MMν = − ⇒
2atmM mν = Δ
Very smallYukawa
couplings!
22 /MF M Mν= Φ
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Dark matter in the νMSM
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Cosmological parameters are well determined now !From CMBR anisotropy
Particle physics candidate“dark” (charge neutral)stable within the age of the universeits abundance should be avoids cosmological constraintsNo candidate in the MSM
Dark energy (77%)
Baryon (4%)Dark matter(19%)
Dark matter
[WMAP ’06]
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Unique candidate: lightest sterile neutrino N1 with ~ keV mass
Cf. Massive active neutrinos cannot be dark matterActive neutrinos are too “hot” (hot dark matter)
Dark matter in the νMSM
Dodelson, Widrow / Shi, Fuller / Dolgov, Hansen / Abazajian, Fuller, Patel
[Hannestad, Raffelt]
But,
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Decays of sterile neutrinoN1 is not completely stable particle !
Dominant decay:Lifetime can be very long
•
N1 is not completely dark !Subdominant decay: Branching ratio is small•
But, severely restricted from X-ray observations
+ …
+ …
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Production of sterile neutrinoTo realize sterile neutrino DM,
How are they produced???
In the early universe,Interaction rate of N1 is very small:• Typically,
We will be interested inN1 is not thermalized !
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Dodelson-Widrow scenario:Production via active-sterile neutrino mixing
Dominant production at
Recently, we improve the estimate of the abundanceUse kinetic equation for density matrixStudy “hadronic uncertainties” in detail:
• Hadronic contributions to production rate• QCD equation of state (time-temp. relation)
Production of sterile neutrino
TA, Laine, Shaposhnikov JHEP06 (’06) 053 [hep-ph/0606209]TA, Laine, Shaposhnikov [hep-ph/0612182]
W,Zνα N
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Relic density of sterile neutrino
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Upper bound on mixing angle
We find
Abazajian: Phys.Rev. D73 (’06) 063506
• The case 1:the largest abundance
the strongest bound
• The case 2:the smallest abundance
the weakest bound
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Constraints from X-rays Radiative decays of sterile neutrino DM
feature in X-ray background spectrumline X-ray from clusters, galaxies, dwarf galaxies…• TEST for sterile neutrino DM!• No signal Upper bound on mixing angle !
Dolgov, Hansen / Abazajian, Fuller, TuckerBoyarsky, Neronov, Ruchayskiy, ShaposhnikovBoyarsky, Neronov, Ruchayskiy, ShaposhnikovBoyarsky, Neronov, Ruchayskiy, Shaposhnikov, TkachevRiemer-Sorensen, Hansen, PedersenWatson, Beacom, Yuksel, WalkerBoyarsky, Ruchayskiy, MarkevitchRiemer-Sorensen, Pedersen, Hansen, DahleAbazajian, Markevitch, Koushiappas, HickoxBoyarsky, Herder, Neronov, Ruchayskiy
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Constraints from structure formationLight sterile neutrino = WDM
Erase structures on smaller scalesLower bound on mass
From Ly-α forest observations
Seljak, Makarov, McDonald, Trac ‘06Viel, Lesgourgues, Haehnelt, Matarresse, Riotto ‘06
We find:
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Parameter spaceX-ray constraint:
Ly-alpha constraint:
Boyarsky, Neronov, Ruchayskiy, Shaposhnikov, Tkachev (astro-ph/0603660)Boyarsky, Nevalainen, Ruchayskiy (astro-ph/0610961)
X-ray constraints from
The Dodelson-Widrowscenario is ruled out in spite of all theoretical uncertainties !
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Fate of sterile neutrino DMDodelson-Widrow scenario assumes:
• No initial abundance at T ~ 1GeV• No new interaction at E < 1GeV• Charge asymmetries smaller than baryon asymmetry
• No low reheating, i.e. RD universe starts T>1GeV
Sterile neutrino DM is still possible, whenLarge lepton asymmetry (Shi-Fuller)
• resonant production via active-sterile oscillationsProduction via decays of Inflaton/Scalar
(Shaposhnikov, Tkachev / Kusenko). . .
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ImplicationsDM sterile neutrino N1must have suppressedYukawa interaction !
What this implies???
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How many sterile neutrinos are needed?We need at least ”two” sterile neutrinos
to explain
In this case, the lightest active neutrino is massless
DM sterile neutrino:
DM sterile neutrino is irrelevant for explaining neutrino mass scales in oscillation experiments
We need at least “three” sterile neutrinos !In this case,
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Active neutrino masses
exclude the degenerate masses of active neutrinos
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Baryogenesis in the νMSM
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Observations:Asymmetry of baryon and
anti-baryon numbers in the universe
This non-zero asymmetry should be generated after, say, the reheating of inflation
Baryogenesis
Three conditions for baryogenesis: SakharovBaryon number violationC and CP violationsOut of equilibrium
Dark energy (77%)
Baryon (4%)Dark matter(19%)
Baryon asymmetry of the universe
11(8.4 8.9) 10Bns
−= − ×
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Baryogenesis conditions in the MSMB and L violation
B and L violations in anomalous EW “sphaleron”which is in thermal equilibrium for T>100GeV
CP violation1 CP phase in the quark-mixing (CKM) matrix
too smallOut of equilibrium
Strong 1st order phase transition ifbutnot satisfied
2 2 2 2 2 2 2 2 2 2 2 2 12 19CPV ( )( )( )( )( )( ) / 10CP t c t u c u b s b d s d EWJ m m m m m m m m m m m m T −∝ − − − − − − ∼
[Kajantie, Laine, Rummukainen, Shaposhnikov]
<72GeVHM114.4GeV (exp.)HM >
We have to go beyond the MSM !!
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Baryogenesis in the νMSMB and L violations
EW sphaleronL violation due to Majorana masses• Now we take Majorana masses < 100 GeV
– Its violating effects can be neglected for high temperatures T>100 GeV
C and CP violations1 CP phase in quark sector6 CP phases in lepton sector• Rich CP violation
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Out of equilibrium
No 1st order EW phase transition as in the MSM
But, sterile neutrinos can be out of equilibriumif Yukawa couplings are small enough
• To ensure this condition up to T~100GeV
• To explain neutrino masses
Baryogenesis conditions in the νMSM
17GeV (atm)M ≤
71,2,3 2 10f −< ×
131[DM: 6 10 ]f −×
Lα
ΦtR QL
N2,3
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The νMSM can potentially realize all three conditions for baryogenesis for T>100GeV
Masses of heavier sterile neutrinos N2 and N3
Is there a realistic scenario ???
Yes !
Baryogenesis in the νMSM
2,31GeV 17GeVM≤ ≤
BBN Out-of-equilibrium
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Sterile neutrinos are created and oscillate with CPV
The total lepton number is zero but is distributed between active and sterile neutrinos
The asymmetry of active left-handed neutrinos is transferred into baryon asymmetry by sphaleron effects
Baryogenesis via neutrino oscillationsAkhmedov, Rubakov, Smirnov ‘98
Idea: Sterile neutrino oscillation is a source of BAU
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Kinetic equation of the systemThe system is described by 12x12 density matrix
Kinetic equation
LL LNLL L N
LL LL LN L N
NL NNN L N N
NL N L NN N N
ρ ρ ρ ρρ ρ ρ ρ
ρρ ρ ρ ρρ ρ ρ ρ
⎛ ⎞⎜ ⎟⎜ ⎟=⎜ ⎟⎜ ⎟⎝ ⎠
†IJ I Ja aρ = 3x3 matrices
{ } { }[ , ] , ,12 2
d pd i ii Hdtρ ρ ρ ρ= − Γ + Γ −
• Effective Hamiltonian including medium effects• Destruction and production rates
H,d pΓ Γ
• Diagonal terms give occupation numbers• Off-diagonal terms contain correlations between states
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First step: at F2 orderN2 and N3 are produced (N1 production is suppressed)
N2 and N3 are oscillate
Lα
ΦtR QL
N2,3
N2
N3
CPV in these processesare suppressed in the νMSM
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Second step: at F4 orderActive flavor asymmetries are generated
but
N2,3
L LN†F F
Evolution rates of and are different due to CPV in
[TA, Shaposhnikov]
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Final step: at F6 orderTotal asymmetries in active and sterile sectors are generated.
but
Evolution rates of and are different due to ΔLα and CPV in N NL
F †F
ΔLεΔLμ
ΔLτ
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Final step: at F6 order (2)Total asymmetries in active and sterile sectors are generated.
but
Evolution rates of ΔLeare different due to different Yukawa couplings
ΔLe
ΔLμ
N2,3
ΔLμ ΔLμL LN
†F F
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Evolution of asymmetries
410 GeVLT ∼
92[10 ]N −Δ
Active sector
6[10 ]Lτ−Δ
6[10 ]eL −Δ
6[10 ]Lμ−Δ
6[10 ]Lμ−Δ
Sterile sector
93[10 ]N −Δ
92[10 ]N −Δ
191[10 ]N −Δ
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• We can generate
• Production starts
Total asymmetries in active and sterile sectors
0, 0but 0
N LN L
Δ ≠ Δ ≠Δ + Δ =
1 2 3N N N NΔ = Δ + Δ + Δ
eL L L Lμ τΔ = Δ + Δ + Δ
28 079
B LΔ = − Δ ≠ Kuzmin, Rubakov, Shaposhnikov
Shaleron converts ΔL partially into baryon asymmetry
410 GeVLT ∼
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Baryon asymmetry of the universe
2/3 5/3510 3
2 232 3
102 10 / 10GeV
BCP
Mns M M
δ−
− ⎛ ⎞ ⎛ ⎞× ⎜ ⎟ ⎜ ⎟Δ ⎝ ⎠⎝ ⎠
( )( ) ( )
( )
4 4 2 223 23 12 13 13 23 23 13 13 2
2 2 213 13 23 23 23 23 2
4 sin
sin
CP R R L L L L L L L L
L L L L L L
s c s s c c s c s
c s s c c s
δ δ α
α
⎡= + − ⋅ +⎣⎤+ − ⋅ ⎦
1 may be possibleCPδ ∼
2 3, 10GeVM M ∼ 3 2 1keVM M M− ∼ ∼
• The effective CP violation parameter
• Heavier sterile neutrinos should be degenerate in mass
in NH 2 23 2, atm solm m m m≈ Δ ≈ Δ
11
OBS
(8.4 8.9) 10Bns
−⎛ ⎞ = − ×⎜ ⎟⎝ ⎠
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III. Summary
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SummaryThe MSM + three right-handed neutrinos (νMSM)
Lightest sterile neutrino ~10keV can be dark matter• The simplest Dodelson-Widrow scenario conflicts with X-ray and Ly-alpha constraints
• Some other production mechanism is needed
Heavier sterile neutrinos can be responsible to baryon asymmetry of the universe• Baryogenesis via neutrino oscillations
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Three sterile neutrinosWe may call as “bright”, “clear” and “dark”
Clear and Bright, NC and NB: Heavier ones• Neutrino oscillations• Baryon asymmetry• M~10GeV, F~10-7, θ~10-6
Dark, ND: Lightest one• Dark matter (production?)• M~keV, F<10-12, θ<10-4
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Neutrino Yukawa coupling constants
†L d RF K P F K Pα β= ⋅ ⋅ ⋅ ⋅
1 2 1 2diag( , ,1), diag( , ,1)i i i iP e e P e eα α β βα β= =
13 13 12 12
23 23 12 12
23 23 13 13
11
1
L
L
iL L L L
L L L L Li
L L L L
c s e c sK c s s c
s c s e c
δ
δ
−⎛ ⎞⎛ ⎞ ⎛ ⎞⎜ ⎟⎜ ⎟ ⎜ ⎟= −⎜ ⎟⎜ ⎟ ⎜ ⎟
⎜ ⎟⎜ ⎟⎜ ⎟− − ⎝ ⎠⎝ ⎠⎝ ⎠13 13 12 12
23 23 12 12
23 23 13 13
11
1
R
R
iR R R R
R R R R Ri
R R R R
c s e c sK c s s c
s c s e c
δ
δ
−⎛ ⎞⎛ ⎞ ⎛ ⎞⎜ ⎟⎜ ⎟ ⎜ ⎟= −⎜ ⎟⎜ ⎟ ⎜ ⎟
⎜ ⎟⎜ ⎟⎜ ⎟− − ⎝ ⎠⎝ ⎠⎝ ⎠
1 2, 3diag( , )dF f f f=
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Averaged momentum
We find:
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Estimation of sterile neutrino abundance
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General formalism
Using density matrix:
Neutrino Yukawa interaction
• Distribution function:
For the production, the leading term is
• Initial condition
•
TA, Laine, Shaposhnikov
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Kinetic equation
1. Dirac neutrino masses:
2. Majorana mass:
3. Self-energy of active neutrinos
calculated within the MSM at finite temperatures
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Active neutrino self-energy
Real part:
negligible
• Generated at 1-loop diagramsof W and Z
• Hadronic contributionsare suppressed by
• is negligibly small compared with 1
• plays a role ofeffective potential
+…
Notzold, Raffelt Enquvist, Kainulainen, Maalampi
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Active neutrino self-energy (2)
Imaginary part:• 1-loop diagrams of W and Z are suppressed by
hadronic uncertainty
• Dominant contributions are 2-loop graphs in the Fermi theory
Hadronic contributions:• We can express these contributions by two point functions
of mesonic currents
• These quantities at T ~ Tc are poorly understood
+…
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Hadronic contributions In general,
“strict” upper bound:
• We estimate by massive free quarks:
Phenomenological approach
“strict” lower bound:
“mean” value:58=d.o.f for four quark flavors
• We may estimate by free quarks for
• We may estimate by the chiral perturbation theory for Dominant pion contributions <1% of leptonic ones
• We expect the hadronic contributions are proportionalto the hadronic degrees of freedom, say
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QCD equation of state
Time-temperature relation:
Laine, SchroderPhenomenological approach
• For high temperaturesperturbative results (resummed 4-loop)
• For low temperaturesa dilute gas of resonances
Kajantie, Laine, Rummukainen, Schroder
• Interpolate two regions smoothly
hadronic uncertainty
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Entropy dilutionDecays of heavier sterile neutrinos can produce entropy by within the νMSM
• Bound from overclosure:
• Bound from X-rays: does not change
• Bound from Ly-α:
Allowed region opens
• Such rate cannot be obtained within the νMSM• Sterile neutrino dark-matter cannot be realized within
the νMSM, if we apply the current Ly-α constraints !!
TA, Kusenko, Shaposhnikov
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Upper bound on mixing angle
We find
Abazajian: Phys.Rev. D73 (’06) 063506
• The case 1:the largest abundance
the strongest bound
• The case 2:the smallest abundance
the weakest bound
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Kinetic equation of the system (2)
We apply the Bolzmann approximation
If the system is in thermal equilibrium,
{ } { }[ , ] , ,2
12
d pd i ii Hdtρ ρ ρ ρ= − Γ + −Γ
{ }[ , ] ,2
d pd ii H idtρ ρ ρ⇒ = − Γ + Γ
{ }1 ,2
p d eqρΓ = Γ{ }[ , ] ,2
d eqd ii Hdtρ ρ ρ ρ⇒ = − Γ −
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Kinetic equation of the system (3)
Effective Hamiltonian
If Dirac Yukawa F=0, the Hamiltonian becomes diagonal
0 intH k H H= + + int :H Contributions from Dirac Yukawa F
0 0 0 0 0( , , , )LL NNL L N NH diag H H H H=
2 220 0 2 2 23 1(1,1,1) ( , , )
32 8W Y
LL eL L
g gTH H diag diag h h hk μ τ
⎡ ⎤+= = +⎢ ⎥
⎣ ⎦0 0 2 2 2
1 2 31 ( , , )
2NN N NH H diag M M Mk
= = Majorana masses
Medium effects
These structures simply the discussion
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Kinetic equation of the system (4)
Let us go to the interaction picture and remove the trivial time dependence due to H0
For Off-diagonal elements of density matrix undergo rapid oscillations and can be put zero due to averaging effectsDiagonal elements must be kept
†U Uρ ρ= ⋅ ⋅ ( )0
0( ) exp ' ( ')
tU t i dt H t= − ∫
Very roughly speaking,
( )0 0exp IJIJ I Ji H H tρ ρ⎡ ⎤− − ⋅⎣ ⎦∼
0 01/( )I Jt H H−
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Kinetic equation of the system (5)
For our interesting time range,
When the effects of sterile neutrino oscillations become important, most of elements are irrelevant.Active neutrinos and charged leptons receive flavor-
dependent effective masses due to
diag diagLL LN LLLL L N LL
diag diagLL LL LN L N LL LL
NL NN NNN L N N N N
NL N L NN N N NN N N
ρ ρ ρ ρ ρ ρρ ρ ρ ρ ρ ρ
ρρ ρ ρ ρ ρ ρρ ρ ρ ρ ρ ρ
⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟= ⇒⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
2 1/3( )PT M M< Δ ⋅
, ,eh μ τ
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Kinetic equation of the system (6)
Since lepton number violation can be neglected,
Only block-diagonal parts are left !
diag diag diagLL LLL Ldiag diag diagLL L L L L
NN NNN N
NN N N N N
ρ ρ ρρ ρ ρ
ρρ ρ ρρ ρ ρ
⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⇒ ⇒⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
Finally, we reach the following equations
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Kinetic equations of the system (7)
[ ] { } †sin ( )4
, ,2
d eqNNNN NN NN NN N LN
eqLL L
i Td iid
FHt
Fρ ρ φ ρ ρρ ρ= − Γ − + ⋅ −
{ } †sin[ , ] , + ( )2 4
diagdiag d diag eq eqLL
LL LL LL LL LL NN NNd i ii H T F F
dtρ φρ ρ ρ ρ ρ= − Γ − ⋅ −
Sterile neutrinos:
Active neutrinos:
• ARS discussed only the terms colored by black• We include the evolution of both sterile and active neutrinos
Let us see the meaning of the each term
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Kinetic equations (2)
[ ] { } †sin, , ( )2 4
d eq eqNNNN NN NN NN NN LL LL
d i ii H T F Fdtρ φρ ρ ρ ρ ρ= − Γ − + ⋅ −
Sterile neutrinos:
0 2 2 21 2 3
1 ( , , )2NNH diag M M M
k=
0 intNN NN NNH H H= +
2int †
8NNTH F F
k=
int2sindNN NNHφΓ = ⋅
N NLF †F
Oscillation Production and destruction2[sin 2 10 ]φ −×
Medium effects
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Kinetic equations (3)
[ ] { } †sin ( )4
, ,2
d eqNNNN NN NN NN N LN
eqLL L
i Td iid
FHt
Fρ ρ φ ρ ρρ ρ= − Γ − + ⋅ −
{ } †[ , sin+ ( )]4
,2
diagdiag d diag eqLL
LL LL LL LL LeqNNL NN
i Td iidt
FH Fφ ρρ ρ ρ ρρ= − Γ − ⋅ −
couple two sectors
• Total lepton number conservation [ ] 0diagNN LL
d Trdt
ρ ρ+ =
• If the system gets thermalized
,eq
NN NNN Nρ ρ ρ→
,eq
LL LLL Lρ ρ ρ→No asymmetry is generated !
( )d HΓ >
[ ] 0diagNN LLTr ρ ρ+ =
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Kinetic equations (3)
[ ] { } †sin ( )4
, ,2
d eqNNNN NN NN NN N LN
eqLL L
i Td iid
FHt
Fρ ρ φ ρ ρρ ρ= − Γ − + ⋅ −
{ } †[ , sin+ ( )]4
,2
diagdiag d diag eqLL
LL LL LL LL LeqNNL NN
i Td iidt
FH Fφ ρρ ρ ρ ρρ= − Γ − ⋅ −
couple two sectors
• Total lepton number conservation [ ] 0diagNN LL
d Trdt
ρ ρ+ =
• If the system gets thermalized
,eq
NN NNN Nρ ρ ρ→
,eq
LL LLL Lρ ρ ρ→No asymmetry is generated !
( )d HΓ >
[ ] 0diagNN LLTr ρ ρ+ =
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Lα
ΦtR QL
N2,3