Matter-Antimatter asymmetry of
the Universe and Leptogenesis
Koichi Hamaguchi (Tokyo U.)@TGSW 2021, September 11, 2021.

Mostly review+ partially based on

K. Asai, KH, N. Nagata, S. Tseng [arXiv:2005.01039], JCAP 11 (2020) 013.
1

Plan

90% of the talk= review• Leptogenesis
Baryon Asymmetry of the Universe
Why “Lepto”genesis?
Seesaw and Leptogenesis in a “big picture”•

Example: Leptogenesis in the minimal gauged U(1)μ−τ model.

• Summary2

Plan

90% of the talk= review• Leptogenesis
Baryon Asymmetry of the Universe
Why “Lepto”genesis?
Seesaw and Leptogenesis in a “big picture”•

Example: Leptogenesis in the minimal gauged U(1)μ−τ model.

• Summary3

In the very early Universe,....
0.000001 sec

１sec
380,000 yrs
1.4 x 1010 yrs
4In the very early Universe,....
The number of particles and anti-particles were almost the same.

matterantimatter5

In the very early Universe,....
The number of particles and anti-particles were almost the same.

But there was tiny excess of matter over anti-matter.

matterantimatter−9

𝒪(10 )

5

In the very early Universe,....
The number of particles and anti-particles were almost the same.

When the Universe got cooler, they pair-annihilated,..

matterantimatter−9

𝒪(10 )

6

In the very early Universe,....
The number of particles and anti-particles were almost the same.

When the Universe got cooler, they pair-annihilated,..

matterantimatter
−9

𝒪(10
)
matter - antimatter annihilationγγ
6

In the very early Universe,....
The number of particles and anti-particles were almost the same.

When the Universe got cooler, they pair-annihilated,..

matterantimatter−9

𝒪(10 )

6

In the very early Universe,....
The number of particles and anti-particles were almost the same.

When the Universe got cooler, they pair-annihilated,..

only matter remains(no antimatter)All of us（Galaxy, the Earth, the human beings,...)are made from this leftover matter.
7

PuzzleHow was the initial excess of matter created ?

matterantimatter−9

𝒪(10 )

8

PuzzleHow was the initial excess of matter created ?

matterantimatter−9

𝒪(10 )

S

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8

Observations (two independent evidences)

9Observations (two independent evidences)(1) Big Bang Nucleosynthesis (BBN)(cosmic time about 1 sec)

24. Big-Bang nucleosynthesis 3

He4
D
Li7
Figure 24.1: The primordial abundances of 4 He, D, 3 He, and 7 Li as predicted by
the standard model of Big-Bang nucleosynthesis—the bands show the 95% CL range[5]. Boxes indicate the observed light element abundances. The narrow verticalband indicates the CMB measure of the cosmic baryon density, while the wider
band indicates the BBN concordance range (both at 95% CL).

[Particle Data Group]10

Observations (two independent evidences)(1) Big Bang Nucleosynthesis (BBN)(cosmic time about 1 sec)

(2) Cosmic Microwave background(cosmic time about 400,000 yrs)
(68%)
[Planck 2015]

They are consistent.
(2) has better precision.

11

When was the Baryon Asymmetry of the Universe generated?

12

When was the Baryon Asymmetry of the Universe generated?
At latest, before the BBN（before 1 sec, temperature > 1 MeV.)
It is difficult to generate the BAU just before the BBN, so usuallymuch earlier time (much higher temperature) is considered.
(An example at a relatively low temperature:
Electroweak Baryogenesis, @ T〜100 GeV.)At earliest, after the Inflation

because the inflation dilutes everything.
(An example just after the inflation: Non-thermal Leptogenesis.
The inflaton decays into right-handed neutrinos, which then lead to Leptogenesis.)13

When was the Baryon Asymmetry of the Universe generated?
time

temperature??

??

Inflation

TR

Reheating

≈

1 sec

100 GeVElectroweak phase transition

1 GeV

QCD phase transition

1 MeV

Big Bang Nucleosynthesis≈
400,000 yrs

24. Big-Bang nucleosynthesis 3

3000 K

Last Scattering Surface≈
14 billion yrs

sometimein this range

CMB
3K

Now
Figure 24.1: The primordial abundances of 4 He, D, 3 He, and 7 Li as predicted by
the standard model of Big-Bang nucleosynthesis—the bands show the 95% CL range[5]. Boxes indicate the observed light element abundances. The narrow verticalband indicates the CMB measure of the cosmic baryon density, while the wider
band indicates the BBN concordance range (both at 95% CL).

14

Standard Model
U

c

t

d

s

b

e

µ

τ

νe

νµ

ντ

h
t
e
Som

... does not work.
g

Z

γ

h

d
n
o
y
e
b
ing

W

Sakharov’s 3 conditions [Sakharov 1967]
Baryon number violation
CP-violation ... (but too small)out-of-equilibrium

n
a
t
S
e
th

e
n
s
i
l
e
d
o
M
d
dar

.
y
r
a
s
s
ce

15

Plan
• Leptogenesis
Baryon Asymmetry of the Universe
Why “Lepto”genesis?
Seesaw and Leptogenesis in a “big picture”•

Example: Leptogenesis in the minimal gauged U(1)μ−τ model.

• Summary
16

Why ”Lepto”genesis?

17

/ L
/ ⇠e
B,
16⇡
2
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✏
µ⌫⇢
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32⇡
Note: B-L is conserved
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Why ”Lepto”genesis?

Within the Standard Model,…

Both Baryon # (B) and Lepton # (L) are conserved at classical level.
µµ@ µ J B = @µ J L = 0

However, B and L are violated at quantum level! [’t Hooft,’76]

TrF
µ⌫

F
⇢

6= 0

µ
µ
@µ (JB JL ) = 0
Although there is essentially no effect at low energy,…

17018

Why ”Lepto”genesis?
Within the Standard Model,…
At high temperature, T >> 100 GeV,
B and L violating processes (sphaleron)become very rapid, and in thermal equilibrium!
[Kuzmin, Rubakov, Shaposhnikov,’85]

Sphaleron processprocesses involving 9 quarks (B=3)
and 3 leptons (L=3).
Note that B-L is conserved.

[fig. from W.Buchmuller, 1210.7758]

19

Therefore, if the Baryon asymmetry is generated via a B-L conserving process,…

e.g, GUT baryogenesis

B=0

L=0

B=100

L=100

20

Therefore, if the Baryon asymmetry is generated via a B-L conserving process,…
Finally B=0 at equilibrium.
e.g, GUT baryogenesis

B=0

L=0

B=100

L=100

B=0

L=0

sphaleron process21

Therefore, if the Baryon asymmetry is generated via a B-L conserving process,…
Finally B=0 at equilibrium.
e.g, GUT baryogenesis

B=0

L=0

B=100

L=100

B=0

L=0

sphaleron process

B-L violating process
is necessary.

21Sakharov’s 3 conditions
・Baryon number (B) violation
・C and CP violation

B-L violation

・Out-of-equilibrium

22

Sakharov’s 3 conditions
・Baryon number (B) violation
・C and CP violation

B-L violation

・Out-of-equilibrium

On the other hand, this means that…
Baryogenesis can work, not only via B-violation,
but also via L-violation.
and L-violation implies Majorana neutrino (and 0νββ decay).
22

Leptogenesis[Fukugita, Yanagida, ’86]

generate Lepton asymmetry
L=-100
B=0

L=0

B=0

right-handed neutrino decay(CP-violating)

N

e

h

≠

N

-e

h

23

Leptogenesis[Fukugita, Yanagida, ’86]

Then, B≠0 remains
at equilibrium!

generate Lepton asymmetry
L=-100
B=0

L=0

L=-65

B=0

B=35

right-handed neutrino decay(CP-violating)sphaleron

N

e

h

≠

N

-e

h

24

Leptogenesis[Fukugita, Yanagida, ’86]

There are various versions…
• Thermal Leptogenesis••[Fukugita, Yanagida,’86, …… Buchmuller, Plumacher, Di Bari,……]

Leptogenesis from Inflaton Decay[…… Asaka, KH, Kawasaki, Yanagida,’99……]

Leptogenesis from R.H.Sneutrino dominated Universe[Murayama, Yanagida,’93, …… KH, Murayama, Yanagida,’01……][Murayama, Suzuki, Yanagida, Yokoyama,’93,… … ]•Affleck-Dine Leptogenesis[Murayama, Yanagida,’93, …… Asaka, Fujii, KH, Yanagida,’00, Fujii, KH, Yanagida,’01, ……]•

via R.H.N oscillation (𝜈MSM)(+ many others …)[Akhmedov, Rubakov, Smirnov,’98, Asaka, Shasposhnikov,’05……]

For reviews, see e.g., arXiv:1711.02861〜 1711.02866.

25

Leptogenesis[Fukugita, Yanagida, ’86]

There are various versions…
• Thermal Leptogenesis•[Fukugita, Yanagida,’86, …… Buchmuller, Plumacher, Di Bari,……]

Leptogenesis from Inflaton Decay[…… Asaka, KH, Kawasaki, Yanagida,’99……]• Model: Standard Model + Right-handed neutrino (very simple!)
Leptogenesis from1R.H.Sneutrino dominated UniverseμYanagida,’93, …… KH, Murayama, Yanagida,’01……]ℒ = ℒSM + NR(iγ ∂μ + [Murayama,
MNR)NR[Murayama,+ yν NRSuzuki,ℓL HYanagida,+ h .Yokoyama,’93,…
c.
…]2
Affleck-Dine Leptogenesis• Boltzmann eqs.
[Murayama, Yanagida,’93, …… Asaka, Fujii, KH, Yanagida,’00, Fujii, KH, Yanagida,’01, ……]
•

•

dNNR

eq
= − D (NNR−NN• )R

via R.H.N oscillation (𝜈MSM)
dz
dNB−L= ϵD (NNR−NNeq) − WNB−L
R (+ many others …)
dz[Akhmedov, Rubakov, Smirnov,’98, Asaka, Shasposhnikov,’05……]•The observed baryon
asymmetry can be
For reviews, see e.g., arXiv:1711.02861〜 1711.02866.
explained if
9
NB−L
MNR ≳ 𝒪(10 ) GeV.
NNR

※ All of them require L-number violation and predict 0νββ decay.
cf. talk by Umehara-san in the previous session.

• Fig. from Buchmuller et.al. [hep-ph/0401240]∼time

Exception: “Dirac leptogenesis”.
[Dick, Lindner, Ratz, Wright, 99,
Murayama, Pierce, 02]26

Leptogenesis[Fukugita, Yanagida, ’86]

There are various versions…
• Thermal Leptogenesis••[Fukugita, Yanagida,’86, …… Buchmuller, Plumacher, Di Bari,……]

Leptogenesis from Inflaton Decay[…… Asaka, KH, Kawasaki, Yanagida,’99……]

Leptogenesis from R.H.Sneutrino dominated Universe[Murayama, Yanagida,’93, …… KH, Murayama, Yanagida,’01……][Murayama, Suzuki, Yanagida, Yokoyama,’93,… … ]•Affleck-Dine Leptogenesis[Murayama, Yanagida,’93, …… Asaka, Fujii, KH, Yanagida,’00, Fujii, KH, Yanagida,’01, ……]•

via R.H.N oscillation (𝜈MSM)(+ many others …)[Akhmedov, Rubakov, Smirnov,’98, Asaka, Shasposhnikov,’05……]

For reviews, see e.g., arXiv:1711.02861〜 1711.02866.

※ All of them require L-number violation and predict 0νββ decay.
cf. talk by Umehara-san in the previous session.

Exception: “Dirac leptogenesis”.
[Dick, Lindner, Ratz, Wright, 99,
Murayama, Pierce, 02]

27

Plan
• Leptogenesis
Baryon Asymmetry of the Universe
Why “Lepto”genesis?
Seesaw and Leptogenesis in a “big picture”•

Example: Leptogenesis in the minimal gauged U(1)μ−τ model.

• Summary28

Seesaw and Leptogenesis in a “big picture”

29Seesaw and Leptogenesis in a “big picture”
Puzzles in the Standard Model= Hints of Physics beyond the Standard Model

Cosmology
Dark Energy
initialcondition of
Universe
Matter >Anti-matter

Dark
MatterParticle Physics
complicatedquark/lepton properties

Higgs
naturalness
strong CP
tiny neutrino mass

30

Seesaw and Leptogenesis in a “big picture”
Puzzles in the Standard Model= Hints of Physics beyond the Standard Model

Cosmology

Particle Physics
complicatedquark/lepton properties

Dark Energy
initialcondition of
Universe
Matter >Anti-matter

Grand Unified
TheoryDark
MatterHiggs
naturalness
strong CP
tiny neutrino mass

Leptogenesis
baryogenesis(heavy) Righthanded neutrino

31

Seesaw and Leptogenesis in a “big picture”
Puzzles in the Standard Model= Hints of Physics beyond the Standard Model

Cosmology

Particle Physics
complicatedquark/lepton properties

Dark Energy
initialcondition of
Universe
Matter >Anti-matter

Grand Unified
TheoryDark
MatterHiggs
naturalness
strong CP
tiny neutrino mass

Leptogenesis
baryogenesis(heavy) Righthanded neutrino

31

Standard Modelleft-handed
quark

(

U

d

right-handed
down quark
right-handed
up quark

left-handed
leptonright-handed
lepton) (- ) (- ) ( ) ( )(3,2)+1/6

LUR(3,1)-2/3

d

R

e

ν

L

(3,1)+1/3 (1,2)-1/2eR(1,1)+1

32

Standard Modelleft-handed
quark

(

U

d

right-handed
down quark
right-handed
up quark

left-handed
leptonright-handed
lepton) (- ) (- ) ( ) ( )(3,2)+1/6

LUR(3,1)-2/3

d

R

e

ν

L

(3,1)+1/3 (1,2)-1/2

Feel weak forceeR(1,1)+1

Don’t feel weak force

32

Standard Modelleft-handed
quark

(

U

d

right-handed
down quark
right-handed
up quark

left-handed
leptonright-handed
lepton) (- ) (- ) ( ) ( )(3,2)+1/6

LUR(3,1)-2/3

d

R

e

ν

L

(3,1)+1/3 (1,2)-1/2

Feel strong
force

Feel weak forceeR(1,1)+1

Don’t feelstrong force

Don’t feel weak force

32

Standard Modelleft-handed
quark

(

U

d

right-handed
up quark

left-handed
leptonright-handed
lepton) (- ) (- ) ( ) ( )(3,2)+1/6

hyper charge

right-handed
down quark

L

U

R

(3,1)-2/3

d

R

e

ν

L

(3,1)+1/3 (1,2)-1/2

Feel strong
force

Feel weak forceeR(1,1)+1

Don’t feelstrong force

Don’t feel weak force

32

Standard Modelleft-handed
quark

(

U

d

right-handed
up quark

left-handed
leptonright-handed
lepton) (- ) (- ) ( ) ( )(3,2)+1/6

hyper charge

right-handed
down quark

L

U

R

(3,1)-2/3

d

R

e

ν

L

(3,1)+1/3 (1,2)-1/2

Feel strong
force

Feel weak forceeR(1,1)+1

Don’t feelstrong force

Don’t feel weak force... very complicated !!
32

Standard Modelleft-handed
quark

(

U

d

right-handed
up quark

left-handed
leptonright-handed
lepton) (- ) (- ) ( ) ( )(3,2)+1/6

hyper charge

right-handed
down quark

L

U

R

(3,1)-2/3

d

R

e

ν

L

(3,1)+1/3 (1,2)-1/2

Feel strong
force

Feel weak forceeR(1,1)+1

Don’t feelstrong force

Don’t feel weak force... very complicated !!
Q: any simple, unified theory to explain it?

32(Standard ModelUd) (- ) (- ) ( ) ( )UL(3,2)+1/6

R(3,1)-2/3

d

R

e

ν

L

(3,1)+1/3 (1,2)-1/2eR(1,1)+1

Q: any simple, unified theory to explain it?

electronic}magnetic

electromagnetic

weakStandard Model}electroweak

strong33(Standard ModelUd) (- ) (- ) ( ) ( )UL(3,2)+1/6

R(3,1)-2/3

d

R

e

ν

L

(3,1)+1/3 (1,2)-1/2eR(1,1)+1

Q: any simple, unified theory to explain it?

electronic}magnetic

electromagnetic

weakStandard Model}strongelectroweak}

Grand Unified
Theory !!

33(Standard ModelUd) (- ) (- ) ( ) ( )UL(3,2)+1/6

R(3,1)-2/3

d

e

R

ν

e

L

(3,1)+1/3 (1,2)-1/2

R(1,1)+1

Q: any simple, unified theory to explain it?

Grand Unified Theory[ SU(5) case ]

(

U

d L

U

10

R

e R

) (

e

ν L

d R

5

)

... beautifully unified
into simple SU(5)representations !

[Georgi, Glashow 1974]34

(Standard ModelUd) (- ) (- ) ( ) ( )UL(3,2)+1/6

R(3,1)-2/3

d

e

R

ν

e

L

(3,1)+1/3 (1,2)-1/2

R(1,1)+1

Q: any simple, unified theory to explain it?
1/3 + 1/3 + 1/3 - 1/2 - 1/2 = 0
Complicated numbers arenaturally explained !

Grand Unified Theory[ SU(5) case ]

(

U

d L

U

10

R

e R

) (

e

ν L

d R

5

)

... beautifully unified
into simple SU(5)representations !

[Georgi, Glashow 1974]

34

Seesaw and Leptogenesis in a “big picture”
Puzzles in the Standard Model= Hints of Physics beyond the Standard Model

Cosmology

Particle Physics
complicatedquark/lepton properties

Dark Energy
initialcondition of
Universe
Matter >Anti-matter

Grand Unified
TheoryDark
MatterHiggs
naturalness
strong CP
tiny neutrino mass

Leptogenesis
baryogenesis(heavy) Righthanded neutrino

35

Seesaw and Leptogenesis in a “big picture”
Puzzles in the Standard Model= Hints of Physics beyond the Standard Model

Cosmology

Particle Physics
complicatedquark/lepton properties

Dark Energy
initialcondition of
Universe
Matter >Anti-matter

Grand Unified
TheoryDark
MatterHiggs
naturalness
strong CP
tiny neutrino mass

Leptogenesis
baryogenesis(heavy) Righthanded neutrino

35

Seesaw and Leptogenesis in a “big picture”
Puzzles in the Standard Model= Hints of Physics beyond the Standard Model

Cosmology

Particle Physics
complicatedquark/lepton properties

Dark Energy
initialcondition of
Universe
Matter >Anti-matter

Grand Unified
TheoryDark
MatterHiggs
naturalness
strong CP
tiny neutrino mass

Leptogenesis
baryogenesis(heavy) Righthanded neutrino

36

puzzle: neutrino masses

(

U

d

) (- ) (- ) ( ) ( )L(3,2)+1/6
left-handed
quark

U

R

(3,1)-2/3

d

R

e

ν

L

(3,1)+1/3 (1,2)-1/2

right-handed
down quark
right-handed
up quarkeR(1,1)+1

right-handed
leptonleft-handed
lepton37

puzzle: neutrino masses

(

U

d

) (- ) (- ) ( ) ( )L(3,2)+1/6
left-handed
quark

U

R

(3,1)-2/3

d

R

e

ν

e

L

(3,1)+1/3 (1,2)-1/2

right-handed
down quark
right-handed
up quark

R(1,1)+1

right-handed
leptonleft-handed
leptonQuarks and leptons have masses by combining
left- and right-handed components (via Higgs, Yukawa interaction).
right-handedeR
Higgs
left-handed eL

Yukawainteraction38

puzzle: neutrino masses

(

U

d

) (- ) (- ) ( ) ( )L(3,2)+1/6
left-handed
quark

U

R

(3,1)-2/3

d

R

e

ν

L

(3,1)+1/3 (1,2)-1/2

right-handed
down quark
right-handed
up quarkeR(1,1)+1

right-handed
leptonleft-handed
lepton

The neutrino has only left-handed component.
===> Massless !!
But the neutrino masses are confirmedby neutrino oscillations.
39

puzzle: neutrino masses

(

U

d

) (- ) (- ) ( ) ( )L(3,2)+1/6
left-handed
quark

U

R

(3,1)-2/3

d

R

e

ν

L

(3,1)+1/3 (1,2)-1/2

right-handed
down quark
right-handed
up quarkeR(1,1)+1

right-handed
leptonleft-handed
leptona solution is ...

40

puzzle: neutrino masses

(

U

d

) (- ) (- ) ( ) ( )L(3,2)+1/6
left-handed
quark

U

R

(3,1)-2/3

d

R

e

ν

L

(3,1)+1/3 (1,2)-1/2

right-handed
down quark
right-handed
up quarkeR(1,1)+1

right-handed
leptonN(1,1)０right-handed
neutrino

left-handed
leptona solution is ...
To add a right-handed neutrino !!
40

The right-handed neutrino N
plays a triple role.

41

The right-handed neutrino N
plays a triple role.

① quarks and leptons completely unified

(

U

d L

U

10

R

e R

) (

e

ν L

5

d R

)

SU(5)
GUT

+

N

(1,1)０42

The right-handed neutrino N
plays a triple role.

① quarks and leptons completely unified

(

U
U

d L

R

e R

) (

e

ν L

10

=

(

)

e

U

d L

5

d R

U

R

e R

16

ν L

dR

N1 R

SU(5)
GUT

+

)

N

(1,1)０SO(10)GUT[Georgi,74
Fritzsch, Minkowski,75]

All quarks andleptons unified !

42

The right-handed neutrino N
plays a triple role.

①=(↑↓ ↓↓↑)
quarks and leptons completely unified(↑↓ ↓↑↓)(↑↓ ↑↓↓)(↓↑ ↓↓↑)(↓↑ ↓↑↓)(↓↑ ↑↓↓)(↑↑ ↑↑↓)(↑↑ ↑↓↑)(↑↑ ↓↑↑)(↓↓ ↑↑↓)(↓↓ ↑↓↑)(↓↓ ↓↑↑)e(↑↓ ↑↑↑)UU R
e R ν LLdR
N R(↓↑ ↑↑↑)d(↑↑ ↓↓↓)
16(↓↓ ↓↓↓)

(

1

) =

43

The right-handed neutrino N
plays a triple role.

② explains tiny neutrino massmasses of quarks and leptons
eV

keV

MeV

GeV

e,µ,τ
quarks(u,d,s,c,b,t)
44

The right-handed neutrino N
plays a triple role.

② explains tiny neutrino massmasses of quarks and leptonseV

neutrinos(ν1, ν2, ν3)

keV

MeV

GeV

e,µ,τ
quarks(u,d,s,c,b,t)
44

The right-handed neutrino N
plays a triple role.

② explains tiny neutrino massmasses of quarks and leptonseV

neutrinos(ν1, ν2, ν3)

keV

MeV

GeV

e,µ,τ
quarks(u,d,s,c,b,t)・・・why neutrino masses are so small??

44

The right-handed neutrino N
plays a triple role.

② explains tiny neutrino mass

(

U

d

) (- ) (- ) ( ) ( )L(3,2)+1/6
left-handed
quark

U

R

(3,1)-2/3

d

R

e

ν

L

(3,1)+1/3 (1,2)-1/2

right-handed
down quark
right-handed
up quarkeR(1,1)+1

right-handed
leptonN(1,1)０right-handed
neutrino

left-handed
lepton45

The right-handed neutrino N
plays a triple role.

② explains tiny neutrino mass

(

U

d

) (- ) (- ) ( ) ( )L(3,2)+1/6
left-handed
quark

U

R

(3,1)-2/3

d

R

e

ν

L

(3,1)+1/3 (1,2)-1/2

right-handed
down quark
right-handed
up quarkeR(1,1)+1

right-handed
leptonN(1,1)０right-handed
neutrino

left-handed
leptonThis guy is special ..... singlet (feels none of three (EM, weak, and strong) forces.)→ it has no charge.
→ it can be its own anti-particle (Majorana particle).
→ it can have a mass without Higgs VEV.

45

The right-handed neutrino N
plays a triple role.

② explains tiny neutrino mass
νL

NR

NR

mass ofright-handed
neutrino

Higgs=(seen e.g., by oscillation exp.)
Neutrino mass

νL

Higgs

(~ Higgs VEV)^2
mass of right-handed neutrino

heavy R.H.ν→ small neutrino masses（“see-saw mechanism”）
46The right-handed neutrino N
plays a triple role.

② explains tiny neutrino mass
νL

NR

NR

mass ofright-handed
neutrino

Higgs=(seen e.g., by oscillation exp.)
Neutrino mass

νL

Higgs

(~ Higgs VEV)^2
mass of right-handed neutrino

heavy R.H.ν→ small neutrino masses（“see-saw mechanism”）
47The right-handed neutrino N
plays a triple role.

② explains tiny neutrino mass
νL

NR

NR

mass ofright-handed
neutrino

Higgs=(seen e.g., by oscillation exp.)
Neutrino mass

νL

Higgs

2
e.g.
(100
GeV
)
(~ Higgs VEV)^2

mass of right-handed neutrino

heavy R.H.ν→ small neutrino masses（“see-saw mechanism”）
47The right-handed neutrino N
plays a triple role.

② explains tiny neutrino mass
νL

NR

NR

mass ofright-handed
neutrino

Higgs=(seen e.g., by oscillation exp.)
Neutrino mass

νL

Higgs

2
e.g.
(100
GeV
)
(~ Higgs VEV)^2

mass of right-handed neutrino

e.g. 1015 GeV

heavy R.H.ν→ small neutrino masses（“see-saw mechanism”）
47The right-handed neutrino N
plays a triple role.

② explains tiny neutrino mass
νL

NR

NR

mass ofright-handed
neutrino

Higgs=(seen e.g., by oscillation exp.)
0.01 eV
Neutrino mass

νL

Higgs

2
e.g.
(100
GeV
)
(~ Higgs VEV)^2

mass of right-handed neutrino

e.g. 1015 GeV

heavy R.H.ν→ small neutrino masses（“see-saw mechanism”）
47The right-handed neutrino N
plays a triple role.

② explains tiny neutrino mass
νL
Higgs

NR

NR

ν…
L a
nd n

eutrin
o
s
b
e
c
>
ome M
p
redictmass ofcf. talk
a
j
s
o
b
r
0
y
right-handed
a
ν
Umeha
n
β
a
β
d
e
ra-sanc
neutrino
a
y
!!
i
n
Higgs
the

=
(seen e.g., by oscillation exp.)
0.01 eV
Neutrino massprevio

2
e.g.
(100
GeV
)
(~ Higgs VEV)^2

use session

mass of right-handed neutrino

e.g. 1015 GeV

heavy R.H.ν→ small neutrino masses（“see-saw mechanism”）
48The right-handed neutrino N
plays a triple role.

③ explains matter > anti-matterasymmetry of the universe.

-----> Leptogenesis !!
right-handed neutrino decay(CP-violating)

N

e

h

≠

N

-e

h
49

Seesaw and Leptogenesis in a “big picture”
Puzzles in the Standard Model= Hints of Physics beyond the Standard Model

Cosmology

Particle Physics
complicatedquark/lepton properties

Dark Energy
initialcondition of
Universe
Matter >Anti-matter

Grand Unified
TheoryDark
MatterHiggs
naturalness
strong CP
tiny neutrino mass

Leptogenesis
baryogenesis(heavy) Righthanded neutrino0νββ decay!!
50

Seesaw and Leptogenesis in a “big picture”
Puzzles in the Standard Model= Hints of Physics beyond the Standard Model

Cosmology

Particle Physics
complicatedquark/lepton properties

Dark Energy
initialcondition of
Universe
Matter >Anti-matter

Grand Unified
TheoryDark
MatterHiggs
naturalness
strong CP
tiny neutrino mass

Leptogenesis
baryogenesis(heavy) Righthanded neutrino0νββ decay!!
50

Seesaw and Leptogenesis in a “big picture”
Puzzles in the Standard Model= Hints of Physics beyond the Standard Model

Cosmology

???

Higgs
naturalness
strong CP
tiny neutrino mass

variousaxion search

inflation

Leptogenesis
baryogenesis

I skip the other parts…

proton decay

complicatedquark/lepton properties

Dark
MatterMatter >Anti-matter

CMB anisotropy,
gravitational wave

Particle Physics

Dark Energy
initialcondition of
Universe

Grand Unified
TheoryCPV in ν-osc.

collider

SUSY?
WIMP

varioussearch(heavy) Righthanded neutrino0νββ decay!!
51

Seesaw and Leptogenesis in a “big picture”
Grand Unified
TheoryPuzzles in the Standard Model= Hints of Physics beyond the Standard Model

Cosmology

???

Dark
MatterMatter >Anti-matter

Higgs
naturalness
strong CP
tiny neutrino mass

variousaxion search

inflation

Leptogenesis
baryogenesis

I skip the other parts…

proton decay

complicatedquark/lepton properties

Dark Energy
initialcondition of
Universe

CMB anisotropy,
gravitational wave

Particle Physics

:
e
t
o
e
r
N
a
e
r
e
h
t

collider

SUSY?
WIMP

varioussearch

n
e
sc

s
o
i
r
a

r
e
h
t
o
(heavy)Rightynamhanded neutrino

CPV in ν-osc.

0νββ decay!!
52

Seesaw and Leptogenesis in a “big picture”
Puzzles in the Standard Model= Hints of Physics beyond the Standard Model

Cosmology

???

Higgs
naturalness
strong CP
tiny neutrino mass

variousaxion search

inflation

Leptogenesis
baryogenesis

I skip the other parts…

proton decay

complicatedquark/lepton properties

Dark
MatterMatter >Anti-matter

CMB anisotropy,
gravitational wave

Particle Physics

Dark Energy
initialcondition of
Universe

Grand Unified
TheoryCPV in ν-osc.

collider

SUSY?
WIMP

varioussearch(heavy) Righthanded neutrino0νββ decay!!
53

Plan
• Leptogenesis
Baryon Asymmetry of the Universe
Why “Lepto”genesis?
Seesaw and Leptogenesis in a “big picture”•

Example: Leptogenesis in the minimal gauged U(1)μ−τ model.

• Summary54

Example: Leptogenesis in the minimal gauged U(1)μ−τ model.
K. Asai, KH, N. Nagata, S. Tseng [arXiv:2005.01039] JCAP 11 (2020) 013
cf. K. Asai, KH, N. Nagata, S. Tseng, K. Tsumura, [arXiv:1811.07571] Phys.Rev. D99 (2019) 055029
K. Asai, KH, N. Nagata, [arXiv:1705.00419] Eur.Phys.J. C77 (2017) 763• gauged U(1)μ−τ model: one of the simplest, anomaly-free extension of the Standard Model.
• In minimal models (with just one scalar) neutrino mass matrix is constrained.

-> predictions!
• Dirac CP phase*mν−1 = *
(*

*
0
*

*
*
0)

• 0νββ double beta decay.

0.027 eV for θ23 ≲ 50.1∘ [1σ, NuFit5.0]⟨mββ⟩ ≳
{0.017 eV for θ23 ≲ 51.7∘ [3σ, NuFit5.0]※ The other parameters are fixed to be the best fit value.
===> testable in the next-generation 0νββ experiments.

55

Example: Leptogenesis in the minimal gauged U(1)μ−τ model.
K. Asai, KH, N. Nagata, S. Tseng [arXiv:2005.01039] JCAP 11 (2020) 013
cf. K. Asai, KH, N. Nagata, S. Tseng, K. Tsumura, [arXiv:1811.07571] Phys.Rev. D99 (2019) 055029
K. Asai, KH, N. Nagata, [arXiv:1705.00419] Eur.Phys.J. C77 (2017) 763• gauged U(1)μ−τ model: one of the simplest, anomaly-free extension of the Standard Model.
• In minimal models (with just one scalar) neutrino mass matrix is constrained.

-> predictions!
•Leptogenesis works.

*mν−1 = *(*• Correlation between the cosmological sign of baryon asymmetry
and the Dirac CP phase of neutrino oscillation.

*
0
*

*
*
0)

δ > π → matter remains
δ < π → anti-matter remains

T2K (global fit)suggests δ > π .

nB /s ≃ 0.87 × 10−10

decay by lightest RHν.

a minimal inflaton decay model.

56

Summary• The Baryon Asymmetry of the Universe = one of the evidences of BSM.
• Leptogenesis can naturally explain it.
• Right-handed neutrino (with large Majorana mass) plays a triple role.
(1). Small neutrino masses. (seesaw)(2). Unification of all quarks and leptons. (16 rep. of SO(10).)(3). Leptogenesis. (matter-antimatter asymmetry)• There are various kinds of Leptogenesis. (Most of them predict 0νββ decay.)• An example: the minimal gauged U(1)μ−τ model. Predictions for neutrino physics.

57

Backup58

What is necessary
to generate the Baryon Asymmetry of the Universe?

59What is necessary
to generate the Baryon Asymmetry of the Universe?

Sakharov’s 3 conditions [Sakharov 1967]
・Baryon number (B) violation
・C and CP violation
・Out-of-equilibrium

60

What is necessary
to generate the Baryon Asymmetry of the Universe?

Sakharov’s 3 conditions [Sakharov 1967]
・Baryon number (B) violation
If all processes conserve B, then impossible to have nB = 0 → nB ≠ 0.

・C and CP violation
・Out-of-equilibrium

61

What is necessary
to generate the Baryon Asymmetry of the Universe?

Sakharov’s 3 conditions [Sakharov 1967]
・Baryon number (B) violation
If all processes conserve B, then impossible to have nB = 0 → nB ≠ 0.

・C and CP violation
If all processes conserve CP, then impossible to have nB = 0 → nB ≠ 0.

・Out-of-equilibrium

62

After inflation
matterantimatter

63

After inflation
matterCP symmetry

antimatterexchange matterand anti-matter

As far as CP is conserved, there isno difference between matter and anti-matter.
63

After inflation
matterCP symmetry

antimatterexchange matterand anti-matter

If CP is violated, there can bea difference between matter and anti-matter.
64

What is necessary
to generate the Baryon Asymmetry of the Universe?

Sakharov’s 3 conditions [Sakharov 1967]
・Baryon number (B) violation
If all processes conserve B, then impossible to have nB = 0 → nB ≠ 0.

・C and CP violation
If all processes conserve CP, then impossible to have nB = 0 → nB ≠ 0.

・Out-of-equilibrium

65

What is necessary
to generate the Baryon Asymmetry of the Universe?

Sakharov’s 3 conditions [Sakharov 1967]
・Baryon number (B) violation
If all processes conserve B, then impossible to have nB = 0 → nB ≠ 0.

・C and CP violation
If all processes conserve CP, then impossible to have nB = 0 → nB ≠ 0.

・Out-of-equilibrium
If the processes nB < 0 ↔︎ nB = 0 ↔︎ nB > 0 are in thermal equilibrium,then the system arrives at the equilibrium state (nB = 0).
The system must be out-of-equilibrium, such that nB = 0

nB > 0.
66

Leptogenesis

67Leptogenesis

Model:[ Fukugita, Yanagida,1986 ]Standard Model + R.H.ν

Cosmology: Standard thermal cosmology
Extremely simple!
No complicated model/cosmology required.
68

Leptogenesis[ Fukugita, Yanagida,1986 ]scenario69

Leptogenesis
scenario

temperature[ Fukugita, Yanagida,1986 ]RHν’s mass

step 1: T > MR : N1 are in thermal bath.

70

Leptogenesis
scenario

temperature[ Fukugita, Yanagida,1986 ]RHν’s mass

step 1: T > MR : N1 are in thermal bath.
step 2: T ∼ MR : N1 decay. (CP violation + out-of-eq.)--> generate Lepton asymmetry, ΔL ≠ 0.

71

Leptogenesis
scenario

temperature[ Fukugita, Yanagida,1986 ]RHν’s mass

step 1: T > MR : N1 are in thermal bath.
step 2: T ∼ MR : N1 decay. (CP violation + out-of-eq.)--> generate Lepton asymmetry, ΔL ≠ 0.

N

e

h

≠

N

-e

h

CP violation
is essential.
71Leptogenesis
scenario

temperature[ Fukugita, Yanagida,1986 ]RHν’s mass

step 1: T > MR : N1 are in thermal bath.
step 2: T ∼ MR : N1 decay. (CP violation + out-of-eq.)--> generate Lepton asymmetry, ΔL ≠ 0.
step 3: Lepton asymmetry
Baryon asymmetry
ΔL ≠ 0--->ΔB ≠ 0(automatic in SM ! thanks to “sphaleron”)[ Kuzmin, Rubakov, Shaposhnikov, 1985 ]72

Leptogenesis
Result:[ Fukugita, Yanagida,1986 ](I skip all the details of the calculation...

For derivations and references, see, e.g., KH: hep-ph/0212305)

73

Leptogenesis
Result:[ Fukugita, Yanagida,1986 ](I skip all the details of the calculation...

For derivations and references, see, e.g., KH: hep-ph/0212305)

73

Leptogenesis
Result:[ Fukugita, Yanagida,1986 ](I skip all the details of the calculation...

For derivations and references, see, e.g., KH: hep-ph/0212305)

final baryon
asymmetry73

Leptogenesis
Result:final baryon
asymmetry[ Fukugita, Yanagida,1986 ](I skip all the details of the calculation...

For derivations and references, see, e.g., KH: hep-ph/0212305)

RHν’s mass73

Leptogenesis
Result:final baryon
asymmetry[ Fukugita, Yanagida,1986 ](I skip all the details of the calculation...

For derivations and references, see, e.g., KH: hep-ph/0212305)

RHν’s mass

heaviest
neutrino mass(〜 atmospheric)73

Leptogenesis
Result:final baryon
asymmetry[ Fukugita, Yanagida,1986 ](I skip all the details of the calculation...

For derivations and references, see, e.g., KH: hep-ph/0212305)

RHν’s mass

heaviest
neutrino mass(〜 atmospheric)wash-out factor (< 1)(calculable: by Boltzmann eq.)73

Leptogenesis
Result:final baryon
asymmetry[ Fukugita, Yanagida,1986 ](I skip all the details of the calculation...

For derivations and references, see, e.g., KH: hep-ph/0212305)

RHν’s mass

wash-out factor (< 1)(calculable: by Boltzmann eq.)heaviest
neutrino mass(〜 atmospheric)

effective
CP violating
phase

73

Leptogenesis
Result:final baryon
asymmetry[ Fukugita, Yanagida,1986 ](I skip all the details of the calculation...

For derivations and references, see, e.g., KH: hep-ph/0212305)

heaviest
neutrino mass(〜 atmospheric)RHν’s masseffective
CP violatingphase

wash-out factor (< 1)(calculable: by Boltzmann eq.)

<1
Yukawa73

Leptogenesis
Result:final baryon
asymmetry[ Fukugita, Yanagida,1986 ](I skip all the details of the calculation...

For derivations and references, see, e.g., KH: hep-ph/0212305)

heaviest
neutrino mass(〜 atmospheric)RHν’s masseffective
CP violatingphase

wash-out factor (< 1)(calculable: by Boltzmann eq.)

<1
YukawaPredictable / Calculable in terms of [SM + R.H.ν] Lagrangian !

73

Leptogenesis
Result:final baryon
asymmetry[ Fukugita, Yanagida,1986 ](I skip all the details of the calculation...

For derivations and references, see, e.g., KH: hep-ph/0212305)

RHν’s mass

wash-out factor (< 1)(calculable: by Boltzmann eq.)heaviest
neutrino mass(〜 atmospheric)

effective
CP violating
phase

74

Leptogenesis
Result:[ Fukugita, Yanagida,1986 ](I skip all the details of the calculation...

For derivations and references, see, e.g., KH: hep-ph/0212305)

final baryon
asymmetry

RHν’s mass

wash-out factor (< 1)(calculable: by Boltzmann eq.)(observed) = (0.88 ± 0.02) x 10-10

heaviest
neutrino mass(〜 atmospheric)

effective
CP violating
phase[PDG, 2012]74

Leptogenesis
Result:[ Fukugita, Yanagida,1986 ](I skip all the details of the calculation...

For derivations and references, see, e.g., KH: hep-ph/0212305)

final baryon
asymmetry

RHν’s mass

wash-out factor (< 1)(calculable: by Boltzmann eq.)(observed) = (0.88 ± 0.02) x 10-10

It works !!

heaviest
neutrino mass(〜 atmospheric)

effective
CP violating
phase[PDG, 2012]910(for MR > 10 -10 GeV).

74