Neutrino masses, dark matterand baryon asymmetry

The νMSM
Takehiko Asaka(Niigata University)@ ICRR, Tokyo Univ.
02 Nov. 2007

Prologue: Physics beyond the MSM
 About 10 years ago …,

z There was no “convincing” evidence for physics
beyond the minimal standard model (MSM)z 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?
•…

Neutrino Oscillations
Cosmic Microwave
Background (CMB)[SuperK][WMAP]

Physics beyond the MSM
 In the last decade(s),we have collected quite“convincing” evidences for physics beyond the MSM
z Neutrino oscillations Æ non-zero neutrino massesz Baryon asymmetryz Dark matterz Dark energyz Scale-invariant density perturbations

Physics beyond the MSM
 In the last decade(s),we have collected quite“convincing” evidences for physics beyond the MSM
z Neutrino oscillations Æ non-zero neutrino massesz Baryon asymmetryz Dark matter?? z Dark energy?? z Scale-invariant density perturbations
 Today, I would like to explain the νMSM, which cansolve first three problems!

OutlinezThe νMSM= the “neutrino” Minimal Standard ModelzDark matter in the νMSM
zBaryogenesis in the νMSM
zSummaryNeutrino oscillations
 Evidence of neutrino oscillations

Æ non-zero neutrino massesz Atmospheric• Atmospheric neutrino exps. (…, SuperK)• Long-baseline accelerator exps. (K2K, MINOS)z Solar• Solar neutrino exps. (…, SuperK, SNO)
• Reactor exp. (KamLand) Need forphysics beyond the minimal standard model (MSM)

The νMSM
 Adding three right-handed neutrinos NI (I=1,2,3)

z 18 new parameters• 3 Majorana masses• 15 parameters in Yukawa coupling matrix– 3 Yukawa couplings– 6 mixing angles– 6 phasesz Dirac and Majorana masses of neutrinos

Seesaw mechanism
 If Majorana masses >> Dirac masses,

⎛ 0
⎜MT
⎝ D

MD ⎞
⎛ Mν
⇒ ⎜
⎟
MM ⎠
⎝ 0

0 ⎞
M M ⎟⎠z active neutrinos
ν 1 , ν 2 , ν 3 (m1 ≤ m2 ≤ m3 )1
Mν = − M
MDMM
M M = diag ( M 1 , M 2 , M 3 )T
DU T Mν U = diag (m1 , m2 , m3 )z sterile neutrinos
N1 , N 2 , N 3 ( M 1 ≤ M 2 ≤ M 3 ) Mixing in CC current

ν α = Uα a ν a + θα I N Ic

(α = e, μ ,τ )(a = 1, 2,3)

θα I = ( M D )α I / M I

1active-sterile mixing

Scale for Majorana mass
 Neutrino oscillations are explained by flavor mixing

between active neutrinos !
z Masses of active neutrinos
1Mν = − M DT
MDMM Where is the scale of Majorana mass ??

z Two “natural” options• Conventional seesaw• The νMSM

Convenstional seesaw scenario: Neutrino Yukawa couplings are comparable to those ofquarks and charged leptonsz MR >> 100GeV• Explain smallness of neutrino masses via seesaw[Yanagida; Gell-Mann, Ramond, Slansky]• Decays of RH neutrino(s) can account for baryon
asymmetry through leptogenesis [Fukugita, Yanagida]• Physics of RH neutrino cannot be tested directly
by experiments

The νMSM:[TA, Blanchet, Shaposhnikov;
TA, Shposhnikov]

 No new mass scale is introducedz MR ~<100GeV• Lightest RH neutrino (~keV) can be DM (?)[Dodelson, Widrow,…]• Oscillation of RH neutrinos can account forbaryon asymmetry of the universe[Akhmedov, Rubakov, Smirnov]• Physics of RH neutrinos can potentially tested byexperiments

Scale of Majorana mass1
Mν = − M
MD ⇒
MM
T
D

F = M M Mν / Φ222Mν = Δmatm

Very small
Yukawacouplings!

Dark matter in the νMSM

Dark matter Cosmological parameters are well determined now !

z From CMBR anisotropy [WMAP ’06]
Dark matter(19%)

 Particle physics candidatez “dark” (charge neutral)z stable within the age of the universez its abundance should bez avoids cosmological constraints
Æ No candidate in the MSM

Baryon (4%)

Dark energy (77%)

Dark matter in the νMSM
 Unique candidate:

lightest sterile neutrino N1 with ~ keV mass
Dodelson, Widrow / Shi, Fuller / Dolgov, Hansen /Abazajian, Fuller, Patel

Cf. Massive active neutrinos cannot be dark matterz Active neutrinos are too “hot” (hot dark matter)[Hannestad, Raffelt]

But,Decays of sterile neutrino
 N1 is not completely stable particle !

z Dominant decay:z Lifetime can be very long•+…

 N1 is not completely dark !

z Subdominant decay:+…
z Branching ratio is small•z But, severely restricted from X-ray observations

Production of sterile neutrino
 To realize sterile neutrino DM,

z How are they produced???
 In the early universe,z Interaction rate of N1 is very small:• Typically,z We will be interested inÆ N1 is not thermalized !

Production of sterile neutrino
 Dodelson-Widrow scenario:z Production via active-sterile neutrino mixing
W,Z

να

N

z Dominant production at Recently, we improve the estimate of the abundancez Use kinetic equation for density matrix
z Study “hadronic uncertainties” in detail:• Hadronic contributions to production rate
• QCD equation of state (time-temp. relation)
TA, Laine, Shaposhnikov JHEP06 (’06) 053 [hep-ph/0606209]
TA, Laine, Shaposhnikov [hep-ph/0612182]

Relic density of sterile neutrinoUpper bound on mixing angle We find• The case 1:

the largest abundance
the strongest bound• The case 2:

the smallest abundance
the weakest boundAbazajian: Phys.Rev. D73 (’06) 063506

Constraints from X-rays
 Radiative decays of sterile neutrino DMz feature in X-ray background spectrum
z line X-ray from clusters, galaxies, dwarf galaxies…
• TEST for sterile neutrino DM!
• No signal Æ Upper bound on mixing angle !
Dolgov, Hansen / Abazajian, Fuller, Tucker
Boyarsky, Neronov, Ruchayskiy, Shaposhnikov
Boyarsky, Neronov, Ruchayskiy, Shaposhnikov
Boyarsky, Neronov, Ruchayskiy, Shaposhnikov,
Tkachev
Riemer-Sorensen, Hansen, Pedersen
Watson, Beacom, Yuksel, Walker
Boyarsky, Ruchayskiy, Markevitch
Riemer-Sorensen, Pedersen, Hansen, Dahle
Abazajian, Markevitch, Koushiappas, Hickox
Boyarsky, Herder, Neronov, Ruchayskiy

Constraints from structure formation
 Light sterile neutrino = WDM

z Erase structures on smaller scalesz Lower bound on mass

 From Ly-α forest observations

Seljak, Makarov, McDonald, Trac ‘06
Viel, Lesgourgues, Haehnelt, Matarresse, Riotto ‘06

We find:Parameter space
 X-ray constraint: Ly-alpha constraint:

The Dodelson-Widrow
scenario is ruled out
in spite of all theoreticaluncertainties !
X-ray constraints from
Boyarsky, Neronov, Ruchayskiy, Shaposhnikov, Tkachev (astro-ph/0603660)
Boyarsky, Nevalainen, Ruchayskiy (astro-ph/0610961)

Fate of sterile neutrino DM
 Dodelson-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, whenz Large lepton asymmetry (Shi-Fuller)• resonant production via active-sterile oscillationsz Production via decays of Inflaton/Scalarz. . .

(Shaposhnikov, Tkachev / Kusenko)

Implications
 DM sterile neutrino N1

must have suppressed
Yukawa interaction !

What this implies???

How many sterile neutrinos are needed?
 We need at least ”two” sterile neutrinos

to explainz In this case, the lightest active neutrino is massless DM sterile neutrino:z DM sterile neutrino is irrelevant for explaining
neutrino mass scales in oscillation experiments
 We need at least “three” sterile neutrinos !

z In this case,Active neutrino masses

exclude the degenerate masses of active neutrinos

Baryogenesis in the νMSM

Baryon asymmetry of the universe
 Observations:

Dark matter(19%)

Baryon (4%)

z Asymmetry of baryon andanti-baryon numbers in the universe
Dark energy (77%)
nB−11= (8.4 − 8.9) × 10s
 This non-zero asymmetry should be generated after,
say, the reheating of inflation
Æ Baryogenesis
 Three conditions for baryogenesis: Sakharov

z Baryon number violationz C and CP violationsz Out of equilibriumBaryogenesis conditions in the MSM
 B and L violationz B and L violations in anomalous EW “sphaleron”
which is in thermal equilibrium for T>100GeV
 CP violationz 1 CP phase in the quark-mixing (CKM) matrix
12
CPV ∝ J CP (mt2 − mc2 )(mt2 − mu2 )( mc2 − mu2 )(mb2 − ms2 )(mb2 − md2 )( ms2 − md2 ) / TEW∼ 10−19

Æ too small Out of equilibriumz Strong 1st order phase transition if M H <72GeV
but M H > 114.4GeV (exp.)[Kajantie, Laine,
Rummukainen, Shaposhnikov]
Æ not satisfied
Æ We have to go beyond the MSM !!

Baryogenesis in the νMSM
 B and L violationsz EW sphaleronz L violation due to Majorana masses• Now we take Majorana masses < 100 GeV– Its violating effects can be neglected for hightemperatures T>100 GeV
 C and CP violationsz 1 CP phase in quark sectorz 6 CP phases in lepton sector• Rich CP violation

Baryogenesis conditions in the νMSM
 Out of equilibriumz No 1st order EW phase transition as in the MSM
z But, sterile neutrinos can be out of equilibrium
if Yukawa couplings are small enough• To ensure this condition up to T~100GeV
Lα
N2,3
−7
f1,2,3 < 2 × 10

[DM: f1

6 × 10−13 ]• To explain neutrino masses

M ≤ 17GeV (atm)

tR

Φ

QL

Baryogenesis in the νMSM
 The νMSM can potentially realize all three conditions

for baryogenesis for T>100GeVz Masses of heavier sterile neutrinos N2 and N3
1GeV ≤ M 2,3 ≤ 17GeVBBN

Out-of-equilibrium Is there a realistic scenario ???

Yes !

Baryogenesis via neutrino oscillations

Akhmedov, Rubakov, Smirnov ‘98

Idea: Sterile neutrino oscillation is a source of BAU
 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 istransferred into baryon asymmetry by sphaleroneffects

Kinetic equation of the system The system is described by 12x12 density matrix⎛ ρ LL⎜ρρ = ⎜ LL
⎜ ρ NL⎜⎝ ρ NL

ρLL
ρLL
ρN L
ρN L

ρ LN
ρ LN
ρ NN
ρ NN

ρL N ⎞
ρ L N ⎟⎟
ρN N ⎟
ρ N N ⎟⎠

ρ IJ = aI† aJ

3x3 matrices• Diagonal terms give occupation numbers• Off-diagonal terms contain correlations between states
 Kinetic equation

dρ
i d
i p
= [ H , ρ ] − {Γ , ρ } + {Γ ,1 − ρ }i22dt• Effective Hamiltonian including medium effects H• Destruction and production rates Γ d , Γ p

 First step: at F2 orderz N2 and N3 are produced (N1 production issuppressed)
Lα
tR

N2,3

Φ

QL

z N2 and N3 are oscillate
N2
N3

CPV in these processes
are suppressedin the νMSM

 Second step: at F4 order[TA, Shaposhnikov]

z Active flavor asymmetries are generated
but

N2,3

Evolution rates ofandare different due to CPV in

L

N
F

†

L

F

 Final step: at F6 orderz Total asymmetries in active and sterile sectors are
generated.
but

ΔLε
ΔLμ
ΔLτ
Evolution rates ofandare different due to ΔLα and CPV in

N

L

F

N
F†

 Final step: at F6 order (2)z Total asymmetries in active and sterile sectors are
generated.
but

ΔLe

N2,3

ΔLμ
L

N
F†

Evolution rates of ΔLe ΔLμ ΔLμ
are different due to different Yukawa couplings

LF

Evolution of asymmetries
Active sector

Sterile sector

ΔN 2 [10−9 ]−6ΔLτ [10 ]ΔN 3 [10−9 ]ΔLμ [10−6 ]ΔLe [10−6 ]ΔN 2 [10−9 ]ΔN1[10−19 ]ΔLμ [10−6 ]TL ∼ 104 GeV

Total asymmetries in active and sterile sectors
ΔN = ΔN1 + ΔN 2 + ΔN 3

• We can generate
ΔN ≠ 0, ΔL ≠ 0
but ΔN + ΔL = 0• Production starts
TL ∼ 104 GeV

ΔL = ΔLe + ΔLμ + ΔLτ
Shaleron converts ΔL partially into baryon asymmetry

28
ΔB = − ΔL ≠ 0
79

Kuzmin, Rubakov, Shaposhnikov

Baryon asymmetry of the universe
nB
s

⎛ 10
⎞
−10
2 ×10 δ CP ⎜
2
2 ⎟
/
Δ
M
M
32
3 ⎠
⎝
−5

2/3

⎛ M3 ⎞⎜ 10GeV ⎟
⎝
⎠

5/ 3

2
2
in NH m3 ≈ Δmatm , m2 ≈ Δmsol• The effective CP violation parameter()δ CP = 4 sR 23cR 23 ⎡ sL12 sL13cL13 ( cL4 23 + sL4 23 ) cL213 − sL213 ⋅ sin (δ L + α 2 )⎣+ cL13 sL213 sL 23cL 23 ( cL2 23 − sL2 23 ) ⋅ sin α 2 ⎦⎤

δ CP ∼ 1 may be possible• Heavier sterile neutrinos should be degenerate in mass
M 2 , M 3 ∼ 10GeV

M 3 − M 2 ∼ keV ∼ M 1⎛ nB ⎞
−11
(8.4
8.9)
10
=
−
×
⎜ ⎟
⎝ s ⎠OBS

III. Summary

Summary The MSM + three right-handed neutrinos (νMSM)

z 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 neededz Heavier sterile neutrinos can be responsible tobaryon asymmetry of the universe• Baryogenesis via neutrino oscillations

Three sterile neutrinos
 We may call as “bright”, “clear” and “dark”

z Clear and Bright, NC and NB: Heavier ones
• Neutrino oscillations• Baryon asymmetry• M~10GeV, F~10-7, θ~10-6
z Dark, ND: Lightest one• Dark matter (production?)• M~keV, F<10-12, θ<10-4

Neutrino Yukawa coupling constants
F = K L ⋅ Pα ⋅ Fd ⋅ K R† ⋅ Pβ
Fd = diag( f1 , f 2, f3 )Pα = diag(eiα1 , eiα 2 ,1), Pβ = diag(eiβ1 , eiβ2 ,1)⎛1
KL = ⎜cL 23⎜⎜− sL 23⎝⎛1
KR = ⎜cR 23⎜⎜− s R 23⎝⎞ ⎛ cL13⎜
sL 23 ⎟ ⎜⎟cL 23 ⎠⎟ ⎝⎜ − sL13eiδ L⎞ ⎛ cR13⎜
sR 23 ⎟ ⎜⎟cR 23 ⎠⎟ ⎜⎝ − s R13eiδ R

sL13e − iδ L ⎞ ⎛ cL12⎟⎜1
⎟ ⎜ − sL12
cL13 ⎟⎠ ⎝⎜sR13e − iδ R ⎞ ⎛ cR12⎟⎜1⎟ ⎜ − sR12
cR13 ⎟⎠ ⎝⎜

sL12
cL12

⎞
⎟
⎟
1 ⎠⎟

sR12
cR12

⎞
⎟
⎟
1 ⎟⎠

Averaged momentum

We find:Estimation ofsterile neutrino abundanceGeneral formalism
TA, Laine, Shaposhnikov
 Using density matrix:• Initial condition• Distribution function:•

Neutrino Yukawa interaction

For the production, the leading term isKinetic equation

1. Dirac neutrino masses:
2. Majorana mass:
3. Self-energy of active neutrinos
calculated within the MSM at finite temperatures

Active neutrino self-energy
 Real part:+…
• Generated at 1-loop diagramsof W and Z• Hadronic contributions
are suppressed by
negligible•is negligibly small
compared with 1•

plays a role ofeffective potential
Notzold, Raffelt
Enquvist, Kainulainen, Maalampi

Active neutrino self-energy (2) Imaginary part:• 1-loop diagrams of W and Z are suppressed by• Dominant contributions are 2-loop graphs in the Fermi theory+…
Hadronic contributions:• We can express these contributions by two point functionsof mesonic currents• These quantities at T ~ Tc are poorly understood

hadronic uncertainty

Hadronic contributions
 In general,• We may estimate by free quarks for• We may estimate by the chiral perturbation theory for
9 Dominant pion contributions <1% of leptonic ones

 Phenomenological approach• We expect the hadronic contributions are proportional
to the hadronic degrees of freedom, say• We estimate by massive free quarks:¾ “strict” upper bound:¾ “strict” lower bound:¾ “mean” value:

58=d.o.f for
four quark flavors

QCD equation of state Time-temperature relation:

hadronic uncertainty
 Phenomenological approach
Laine, Schroder• For high temperatures
perturbative results (resummed 4-loop)
Kajantie, Laine, Rummukainen, Schroder• For low temperatures
a dilute gas of resonances• Interpolate two regions smoothlyEntropy dilution
 Decays of heavier sterile neutrinos can produce

entropy by

within the νMSM

TA, Kusenko, Shaposhnikov• 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 withinthe νMSM, if we apply the current Ly-α constraints !!

Upper bound on mixing angle
 We find• The case 1:
the largest abundance
the strongest bound• The case 2:
the smallest abundance
the weakest boundAbazajian: Phys.Rev. D73 (’06) 063506

Kinetic equation of the system (2) We apply the Bolzmann approximation
i

dρ
i
i
= [ H , ρ ] − {Γ d , ρ } + {Γ p ,1 − ρ }
dt
2
2

⇒i

dρ
i
= [ H , ρ ] − {Γ d , ρ } + iΓ pdt
2

 If the system is in thermal equilibrium,

dρ
i d
⇒i
= [ H , ρ ] − {Γ , ρ − ρ eq }dt
2

1 d eqΓ = {Γ , ρ }2pKinetic equation of the system (3) Effective HamiltonianH = k + H 0 + H int

H int : Contributions from Dirac Yukawa F

 If Dirac Yukawa F=0, the Hamiltonian becomesdiagonal00
H 0 = diag ( H LL
, H L0 L , H NN
, H N0 N )Medium effects

2
2
2
⎡
3
g
g
+
T
1
0
0
2
2
2 ⎤
W
Y
H LL = H L L =diag (1,1,1) + diag (he , hμ , hτ ) ⎥⎢8k ⎣ 32⎦1
00
H NN = H N N =diag ( M 12 , M 22 , M 32 )Majorana masses
2k

These structures simply the discussion

Kinetic equation of the system (4) Let us go to the interaction picture and remove thetrivial time dependence due to H0

ρ = U ⋅ ρ ⋅U

†

(

t

U (t ) = exp −i ∫ dt ' H 0 (t ')0)Very roughly speaking,ρ IJ ∼ exp ⎡⎣ −i ( H I0 − H J0 ) t ⎤⎦ ⋅ ρ IJ
 For

t

1/( H I0 − H J0 )zOff-diagonal elements of density matrix undergo rapid
oscillations and can be put zero due to averaging
effectszDiagonal elements must be kept

Kinetic equation of the system (5) For our interesting time range, T < ( ΔM 2 ⋅ M P )1/ 3⎛ ρ LL⎜ρρ = ⎜ LL
⎜ ρ NL⎜⎝ ρ NL

ρLL
ρLL
ρN L
ρN L

ρ LN
ρ LN
ρ NN
ρ NN

diag
ρ L N ⎞ ⎛ ρ LL
⎜ diag
ρ L N ⎟⎟ ⎜ ρ LL⇒
ρN N ⎟ ⎜⎜ρ N N ⎟⎠ ⎜⎝ρ LdiagLρ Ldiag
L

ρ NN
ρ NN

⎞
⎟
⎟
ρN N ⎟⎟⎟
ρN N ⎠

zWhen the effects of sterile neutrino oscillations
become important, most of elements are irrelevant.
z Active neutrinos and charged leptons receive flavordependent effective masses due to he,μ ,τKinetic equation of the system (6) Since lepton number violation can be neglected,
diag⎛ ρ LL⎜ diag
ρ LL
⎜
ρ⇒
⎜
⎜⎜
⎝

ρ LdiagLρ Ldiag
L

ρ NN
ρ NN

diag
⎞ ⎛ ρ LL⎟ ⎜⎟⇒⎜
ρN N ⎟ ⎜⎟⎟ ⎜⎜ρN N ⎠ ⎝ρ LdiagLρ NN

zOnly block-diagonal parts are left !
Finally, we reach the following equations

⎞
⎟
⎟
⎟
⎟⎟
ρN N ⎠

Kinetic equations of the system (7)Sterile neutrinos:d ρ NNi sin φi deq
= [ H NN , ρ NN ] − {Γ NN , ρ NN − ρ NN } +T ⋅ F † ( ρ LL − ρ LeqL ) F
i24
dt
Active neutrinos:
diagd ρ LLii sin φ
diag
diag
eq
eq
= [ H LL , ρ LL
− ρ LL] − {Γ dLL , ρ LL+
)F †i
T ⋅ F ( ρ NN − ρ NN
}
2
4
dt

• 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

Kinetic equations (2)Sterile neutrinos:d ρ NNi di sin φeqeq
= [ H NN , ρ NN ] − {Γ NN , ρ NN − ρ NN } +)FiT ⋅ F † ( ρ LL − ρ LL
2
4
dt
Oscillation

H NN = H
H

0
NN

0
NN

+H

Production and destruction

int
NN

Γ

d
NN

= 2sin φ ⋅ H

intNN[sin φ2 × 10−2 ]1=diag ( M 12 , M 22 , M 32 )
2k

2
T
int
H NN
=
F †F
8k

Medium effects

N

L

F

N
F†

Kinetic equations (3)couple two sectorsd ρ NNi sin φi deq
= [ H NN , ρ NN ] − {Γ NN , ρ NN − ρ NN } +T ⋅ F † ( ρ LL − ρ LeqL ) F
i
2
4
dt
diag
d ρ LLi sin φ
i d
diag
diag
eq
eq
= [ H LL , ρ LL ] − {Γ LL , ρ LL − ρ LL } +)F †T ⋅ F ( ρ NN − ρ NN
i
2
4
dt

• Total lepton number conservation

d
diag
]=0
Tr[ ρ NN + ρ LL
dt

• If the system gets thermalized (Γ d > H )eqρ NN , ρ N N → ρ NNeq
ρ LL , ρ L L → ρ LL

No asymmetry is generated !
diag
Tr[ ρ NN + ρ LL]=0

Kinetic equations (3)couple two sectorsd ρ NNi sin φi deq
= [ H NN , ρ NN ] − {Γ NN , ρ NN − ρ NN } +T ⋅ F † ( ρ LL − ρ LeqL ) F
i
2
4
dt
diag
d ρ LLi sin φ
i d
diag
diag
eq
eq
= [ H LL , ρ LL ] − {Γ LL , ρ LL − ρ LL } +)F †T ⋅ F ( ρ NN − ρ NN
i
2
4
dt

• Total lepton number conservation

d
diag
]=0
Tr[ ρ NN + ρ LL
dt

• If the system gets thermalized (Γ d > H )eqρ NN , ρ N N → ρ NNeq
ρ LL , ρ L L → ρ LL

No asymmetry is generated !
diag
Tr[ ρ NN + ρ LL
]=0

Lα
tR

N2,3

Φ

QL