Leptogenesis via 4th Dec 2018 active neutrino oscillation 1. - - PowerPoint PPT Presentation

Leptogenesis via active neutrino oscillation

Wen Yin, KAIST in Korea

1807.06582 with Ryuichiro Kitano, and Yuta Hamada

comic by Yuki Yamamoto, 
 higgstan.com

@ KEKPH with 3rd KIAS-NCTS-KEK Joint Workshop 4th Dec 2018

• 1. Introduction

Sakharov’s conditions

*Baryon/Lepton number violation *C and CP violation *Out of thermal equilibrium

How to generate the baryon asymmetry?

Unfortunately, the SM does not sufficiently satisfy…

• 1. Introduction

Sakharov’s conditions

*Baryon/Lepton number violation *C and CP violation *Out of thermal equilibrium

The SM (probably) is an effective theory with Majorana neutrino mass term

A clear New Physics! Neutirno mass

How to generate the baryon asymmetry?

Unfortunately, the SM does not sufficiently satisfy…

• 1. Introduction

Sakharov’s conditions

*Baryon/Lepton number violation *C and CP violation *Out of thermal equilibrium

The SM (probably) is an effective theory with Majorana neutrino mass term

✔

A clear New Physics! Neutirno mass

How to generate the baryon asymmetry?

Unfortunately, the SM does not sufficiently satisfy…

3

Neutrino Oscillation Provides CP violation.

(If PMNS matrix has a dirac CP phase)

νe

νµ

UPMNS ⌘ hνi|ναi

T2K Collaboration, 1701.00432 Observerd at 2sigma level

Pνe→νµ ' | X

α

hνe|ναieitm2

να/khνα|νµi|2

P¯

νe→¯ νµ ' |

X

α

hνe|ναie−itm2

να/khνα|νµi|2

CP conjugate

3

Neutrino Oscillation Provides CP violation.

(If PMNS matrix has a dirac CP phase)

νe

νµ

6=

UPMNS ⌘ hνi|ναi

CP violation!

T2K Collaboration, 1701.00432 Observerd at 2sigma level

Pνe→νµ ' | X

α

hνe|ναieitm2

να/khνα|νµi|2

P¯

νe→¯ νµ ' |

X

α

hνe|ναie−itm2

να/khνα|νµi|2

Different

*Baryon/Lepton number violation *C and CP violation ✔ *Out of thermal equilibrium

✔ Neutrino oscillation can provide CP violation

Introduction

Sakharov’s conditions

How to generate the baryon asymmetry?

The SM (probably) is an effective theory with Majorana neutrino mass term

A clear New Physics! Neutirno mass

*Baryon/Lepton number violation *C and CP violation ✔ *Out of thermal equilibrium

✔ Neutrino oscillation can provide CP violation

Introduction

Sakharov’s conditions

How to generate the baryon asymmetry?

The SM (probably) is an effective theory with Majorana neutrino mass term

A clear New Physics! Neutirno mass

Thermalization, such as in reheating era.

✔

5

Thermal Plasma e.g. a neutrino

• ut of equilibrium

Flavor oscillation of high energy leptons during reheating era can generate lepton asymmetry in a different model.

Kitano, Hamada, 1609.05028

Flavor oscillation during thermalization.

f l a v

• r
• s

c i l l a t i

• n

CP violation During thermalization llHH interaction

What we found

Enough baryon asymmetry created during thermalization from neutrino osc. within SM +

• Baryogenesis could be possible in any UV models 


leading to the effective SM.

• Testable in neutrino exps.

e.g. from integrating out heavy particles such as right-handed neutrino

Yanagida 79; Gell-Mann, et al 79; Minkowski, 77; Glashow, 80; Mohapatra and Senjanovic, 80; ( WY, 1808.00440, byproduct

• f charge quantization due to SUSY)

Kitano, Hamada, WY 1807.06582

• The quantum effect is included systematically 


by using kinetic equation.

7

• 2. Leptogenesis via active oscillation

ν

7

Thermal Plasma e.g. a neutrino

• ut of equilibrium

f l a v

• r
• s

c i l l a t i

• n

CP violation During thermalization llHH interaction

8

Kinetic Equation (Extended Boltzmann Eq)

density matrix for left-handed leptons

Ωij(p)

Sigl, Raffelt, 1993
 — — — —

− [Ω(p), ¯ ρ(p)]

Hamiltonian:

Interaction terms (with CP phase)

ρ(p) ≡ ρij(p)

i, j = e, µ, τ

This is absent in ordinary Boltzmann eqs.

Kitano, Hamada, WY,1807.06582 Oscillation term

8

Kinetic Equation (Extended Boltzmann Eq)

density matrix for left-handed leptons

Ωij(p)

Sigl, Raffelt, 1993
 — — — —

− [Ω(p), ¯ ρ(p)]

Hamiltonian:

Interaction terms (with CP phase)

Oscillation term generates flavor dependent lepton asymmetry,

but ρ(p) ≡ ρij(p)

i, j = e, µ, τ

This is absent in ordinary Boltzmann eqs.

Different Kitano, Hamada, WY,1807.06582

tr[ ˙ ρ − ˙ ¯ ρ] ∼ 0

9

CASE A: Inflaton decay to Leptons flavor dependently

Inflaton

→

TR, mφ, B, Vi

Parameters

and V e| lei + V µ| lµi + V τ| lτi , (V e)∗| ¯ le ↵ + (V µ)∗| ¯ lµ ↵ + (V τ)∗| ¯ lτ ↵

@ Branching ratio=B mνlightest

δ, αM, βM

for two mass ordering

10

mφ/TR = 1

mφ/TR = 100

Dirac phase=-pi/2, Majorana phase=0.3 pi, Required

8 9 10 11 12 13 14 15 16 10-11 10-9 10-7 10-5 10-3 Log10[TR/GeV] |nL|/s/B

φ → leptons

This scenario works for TR & 108 GeV

By solving (approximated) kinetic equations for leptons, we get

Solution (Normal Hierarchy)

V∝{1,1,1}

10

mφ/TR = 1

mφ/TR = 100

Dirac phase=-pi/2, Majorana phase=0.3 pi, Required

8 9 10 11 12 13 14 15 16 10-11 10-9 10-7 10-5 10-3 Log10[TR/GeV] |nL|/s/B

φ → leptons

This scenario works for TR & 108 GeV

By solving (approximated) kinetic equations for leptons, we get

Solution (Normal Hierarchy)

V∝{1,1,1}

11

∆33/s ≡

• U −1

PMNS(ρ − ¯

ρ)UPMNS

• 33

∆33/s/B

−nL/s/B

nL/s ≡ Tr[ρ − ¯ ρ + ...]

10-5 10-4 0.001 0.010 0.100 1 10-15 10-12 10-9 10-6 t×H(TR)

11

Flavor dependent asymmetry but Oscillation

∆33/s ≡

• U −1

PMNS(ρ − ¯

ρ)UPMNS

• 33

∆33/s/B

−nL/s/B

nL/s ≡ Tr[ρ − ¯ ρ + ...]

10-5 10-4 0.001 0.010 0.100 1 10-15 10-12 10-9 10-6 t×H(TR)

nL/s ' ∆33 + ∆22 + ∆11 ⇠ 0

11

Flavor dependent asymmetry but Oscillation (net) Asymmetry Production

∆33/s ≡

• U −1

PMNS(ρ − ¯

ρ)UPMNS

• 33

∆33/s/B

−nL/s/B

nL/s ≡ Tr[ρ − ¯ ρ + ...]

(Γwo)α ∝ m2

να

Normal hierarchy: is largest.

(Γwo)3

∆33/s/B

−nL/s/B

Washout

10-5 10-4 0.001 0.010 0.100 1 10-15 10-12 10-9 10-6 t×H(TR)

nL/s ' ∆33 + ∆22 + ∆11 ⇠ 0

11

Flavor dependent asymmetry but Flavor is “observed” via Yukawa interaction Oscillation (net) Asymmetry Production “Observation”

∆33/s ≡

• U −1

PMNS(ρ − ¯

ρ)UPMNS

• 33

∆33/s/B

−nL/s/B

nL/s ≡ Tr[ρ − ¯ ρ + ...]

(Γwo)α ∝ m2

να

Normal hierarchy: is largest.

(Γwo)3

∆33/s/B

−nL/s/B

Washout

10-5 10-4 0.001 0.010 0.100 1 10-15 10-12 10-9 10-6 t×H(TR)

nL/s ' ∆33 + ∆22 + ∆11 ⇠ 0

Neutrino Magic

ν1, ν2, ν3

¯ ν3, ¯ ν2, ¯ ν1

Baryon asymmetry could be explained by any model leading to

L = LSM + κllHH + ...

@ µRG > 108GeV

13

CASE B: Inflaton dominantly 
 decay to Higgs boson

αM π/2 αM=π/4 αM=0 αM=-π/4 αM=-π/2 12 13 14 15 16 10-11 10-10 10- 10- 10- Log10[

R/GeV]

|nL|/s

Normal hierarchy one massless neutrino.

δ = −π/2

14

• 4.0
• 3.5
• 3.0
• 2.5
• 2.0
• 1.5
• 1.0

10-4 0.001 0.010 0.100 1 log10(mνlightest/eV) mνee [eV]

δ=-3π/4, TR≤1013GeV

Neutrinoless double beta decay

The CP phase and neutrino mass can be tested from neutrino exps.

Summary

• The observed asymmetry can be explained at 


reheat temp >

• The scenario can be tested in future neutrino exps,

especially for inflaton dominantly decays to Higgs.

Kitano, Hamada, WY,1807.06582

Baryon asymmetry explained within SM with

108 GeV

16

Backups

17

Ωij(p)

Two scales approximation, p ∼ mφ, p ∼ T

Some formula can be also found in Akhmedov,et al. 9803255; Abada, et al. 0601083.; Asaka, et al. 1112.5565. See Refs. [Landau and Pomeranchuk 1953; Migdal 1956] for LPM effect.

Kinetic Equations to be solved

and eqs for CP conjugate process
 and right-handed leptons

18

Initial condition

Inflaton

→

TR, mφ, B, Vi

Parameters

and those for neutrino oscillation. V e| lei + V µ| lµi + V τ| lτi , (V e)∗| ¯ le ↵ + (V µ)∗| ¯ lµ ↵ + (V τ)∗| ¯ lτ ↵

CASE A

19

CASE B

Initial conditions

Inflaton →

TR, mφ, B

and those for neutrino oscillation. Higgs, Higgs* →

l, ¯ l

ρT |t=tR = ¯ ρT |t=tR = 0

Parameters

(Leptons are not thermalized initially)

L ⊃ Aφ|H|2

20

Not complete washout with degenerate case

sym.

Conserved current for lepton flavor sym. Certain flavor dependent asymmetry remains. Even with very high Temp, conserved current protects lepton asymmetry!

κ ' 1/v2diag[mν, mν, mν]

SO(3)

21

Oscillation phase

t−1

scat ∼ α2 2T ∼ 109

✓ T 1012GeV ◆ GeV

t−1

• sc ∼ y2

τ

16T ∼ 107 ✓ T 1012GeV ◆ GeV

Phase ⇠ t−1

• sctscat ⌧ 1

Coherently scattering (LPM effect) becomes important and it is included in the analysis.

22

FIGURES FOR INFLATON->LEPTON

23

8 9 10 11 12 13 14 15 16 10-11 10-9 10-7 10-5 10-3 Log10[TR/GeV] |nL|/s/B

normal hierarchy one massless neutrino. Other parameters are same as the main part one.

24

8 9 10 11 12 13 14 15 16 10-11 10-9 10-7 10-5 10-3 Log10[TR/GeV] |nL|/s/B

normal order degenerate mass. mnulightest=0.07eV Other parameters are same as the main part one.

25

8 9 10 11 12 13 14 15 16 10-11 10-9 10-7 10-5 10-3 Log10[TR/GeV] |nL|/s/B

inverted order degenerate mass. mnulightest=0.07eV Other parameters are same as the main part one.

26

FIGURES FOR INFLATON->HIGGS

27

αM=π/2 αM=π/4 αM=0 12 13 14 15 16 10-11 10-10 10-9 10-8 10-7 Log10[TR/GeV] |nL|/s

28

αM π/2 11 12 13 14 15 16 10-11 10-10 10- 10- 10- 10-6 Log10[

R/GeV]

|nL|/s

Inverted degenerate case. mnulightest=0.07eV

29

αM π/2 αM=π/4 αM=0 αM=-π/4 αM=-π/2 11 12 13 14 15 16 10-11 10-10 10- 10- 10- 10-6 Log10[

R/GeV]

|nL|/s

Normal hierarchy degenerate case. mnulightest=0.07eV

30

• 3
• 2
• 1

1 2 3 1.×10-11 5.×10-11 1.×10-10 5.×10-10 1.×10-9 δ |nL|/s/B

αM=0 αM=-π/2 αM=-π/4 αM=π/4 αM=π/2

Inverted, TR=mϕ/100=4×1012GeV, mνlightest=0eV

31

• 3 -2 -1

1 2 3 5.×10-11 1.×10-10 5.×10-10 1.×10-9 5.×10-9 δ |nL|/s/B

αM=0 αM=-π/2 αM=-π/4 αM=π/4 αM=π/2

Inverted, TR=mϕ/100=7×1011GeV, mνlightest=0.07eV

32

• 3
• 2
• 1

1 2 3

• 5. ×10-11
• 1. ×10-10
• 5. ×10-10
• 1. ×10-9
• 5. ×10-9

δ |nL|/s/B

αM=0 αM=-π/2 αM=-π/4 αM=π/4 αM=π/2

Normal, TR =mϕ/100=7×1011GeV, mνlightest=0.07eV

33

• 3
• 2
• 1

1 2 3

• 1. ×10-11
• 5. ×10-11
• 1. ×10-10
• 5. ×10-10
• 1. ×10-9

δ |nL|/s

αM=0 αM=-π/2 αM=-π/4 αM=π/4 αM=π/2

Inverted, TR =mϕ/100=1016GeV, mνlightest=0

34

• 3
• 2
• 1

1 2 3

• 1. ×10-11
• 5. ×10-11
• 1. ×10-10
• 5. ×10-10
• 1. ×10-9

δ |nL|/s

αM=0 αM=-π/2 αM=-π/4 αM=π/4 αM=π/2

Inverted, TR =mϕ/100=4×1015GeV, mνlightest=0.07eV

35

• 3
• 2
• 1

1 2 3

• 1. ×10-11
• 5. ×10-11
• 1. ×10-10
• 5. ×10-10
• 1. ×10-9

δ |nL|/s

αM=0 αM=-π/2 αM=-π/4 αM=π/4 αM=π/2

Normal, TR =mϕ=1015GeV, mνlightest=0eV

36

• 3
• 2
• 1

1 2 3

• 1. ×10-11
• 5. ×10-11
• 1. ×10-10
• 5. ×10-10
• 1. ×10-9

δ |nL|/s

αM=0 αM=-π/2 αM=-π/4 αM=π/4 αM=π/2

Normal, TR =mϕ/100=4×1015GeV, mνlightest=0.07eV

37

• 4.0
• 3.5
• 3.0
• 2.5
• 2.0
• 1.5
• 1.0

10-4 0.001 0.010 0.100 1 log10(mνlightest/eV) mνee [eV]

δ=-3π/4, TR≤1013GeV