1/341/34

Baryogenesis by B - L generation due to superheavy particle decay

Seishi Enomoto ( Nagoya Univ, Japan )

Based on : Phys. Rev. D 84, 096007 (2011),S. E. and Nobuhiro Maekawa (Nagoya Univ., KMI Inst.)

2013/3/20 The IOPAS HEP Theory Journal Club ＠ Academia Sinica

2/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

1. Introduction

2. B – L violating particles and interactions

3. B – L number generation and bound of parameter

4. Summary

2013/3/20

Contents

1. Introduction

aboutour

study

3/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Introduction

In the present Universe Matters 　 >> 　 Anti-matters # Photons 　 >> 　 # Baryons (matters)

The observation (WMAP) 　　

　　　 ( E. Komatsu [WMAP Collaboration] , Astrophys. J. Suppl. 192, 18 (2011) )

In the Early Universe : High temperature (the thermal fluctuation) There exists very small asymmetry between baryons and anti-baryons.

2013/3/20

Baryons

Anti- baryons

Photons

⟸ (𝑛𝐵−𝑛𝐵 ) /𝑛𝛾

Baryogenesis

Not initial conditionBut dynamical

generation

1. Introduction

4/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Sakharov’s 3 conditions

1. #B number violation It is necessary by the definition.

2. C & CP violation Baryon asymmetries do not

evolve if there is no difference between particles and anti-particles.

3. Non-equilibrium condition Baryon asymmetries do not

evolve if the forward and back reaction rate is equal.

2013/3/20

[ A. D. Sakharov (1967) ]

b

b

b𝑋

l𝑋

𝐵=+2/3

𝐵=−1/3

+1/3

+1/3

0

−1 /3

Conditions to be evolved from to of the Universe.

1. Introduction

decay

decay

5/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Sakharov’s 3 conditions

1. #B number violation It is necessary by the definition.

2. C & CP violation Baryon asymmetries do not

evolve if there is no difference between particles and anti-particles.

3. Non-equilibrium condition Baryon asymmetries do not

evolve if the forward and back reaction rate is equal.

2013/3/20

[ A. D. Sakharov (1967) ]

bbX bbX

bllbX X

** C, CP invariant case **

Branchingratio

1. Introduction

𝑋 𝑏 ,𝑏𝑏 , 𝑙

Conditions in order to be evolved from to of the Universe.

50 %

50 %

50 %

50 %

6/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Sakharov’s 3 conditions

1. #B number violation It is necessary by the definition.

2. C & CP violation Baryon asymmetries do not

evolve if there is no difference between particles and anti-particles.

3. Non-equilibrium condition Baryon asymmetries do not

evolve if the forward and back reaction rate is equal.

2013/3/20

[ A. D. Sakharov (1967) ]

** C, CP invariant case **

Branchingratio

bbX

1. Introduction

𝑋 𝑏 ,𝑏𝑏 , 𝑙

Conditions in order to be evolved from to of the Universe.

50 %

50 %

0 %

100 %

blX

bllbX X#B is

remained.

7/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Sakharov’s 3 conditions

1. #B number violation It is necessary by the definition.

2. C & CP violation Baryon asymmetries do not

evolve if there is no difference between particles and anti-particles.

3. Non-equilibrium condition Baryon asymmetries do not

evolve if the forward and back reaction rate is equal.

2013/3/20

[ A. D. Sakharov (1967) ]

b

bX

Suppression of the back reaction

1. Introduction

Conditions in order to be evolved from to of the Universe.

#B is remaine

d.

8/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Models of baryogenesis

GUT baryogenesis

Leptogenesis

Electro weak baryogenesis

Affleck Dine baryogenesis

etc...

2013/3/20 1. Introduction

9/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Models of baryogenesis

GUT baryogenesis The minimal SU(5) GUT baryogenesis

SM particles 　＋　 gauge bosons 　＋　 Colored Higgs　　⇒　 # ， # violating interactions However, since # is conserved, it is known that the generated # is washed out by

the sphaleron process induced after age.

Leptogenesis Thermal leptogenesis

SM particles 　＋　 Right handed neutrinos　　⇒　 # is conserved, but #, # are violated. After that, a part of # is converted to # by the sphaleron process.

★ Both models are heavy particles decay scenario, and more, just simple.

★ Deciding the success is whether # is violated or not.

2013/3/20

𝑳𝑩

𝑳

1. Introduction

[ M. Yoshimura (1978), S. Weinberg (1979) , etc. ]

[ M. Fukugita, T. Yanagida (1986) ]

Is there any possibilities to

generate #B - L with heavy particles?

10/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

1. Introduction

2. B – L violating particles and interaction

3. B – L number generation and bound of parameter

4. Summary

2013/3/20

Contents

aboutour

study

1. Introduction 2. B – L violating particle & int.

11/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary2013/3/20

Decomposition of the , violating interactions

There exists , in the higher dimensional interactions.decomposition of a interaction obtationed or ⇒ particles and interactions

dim. 5 :

　　　　　　⇒　 Leptogenesis dim. 6 :

　　　 ⇒　 GUT baryogenesis★ We can obtain the scenario to generate # to decompose the violating higher dimensional interactions!

𝑳

𝑳

𝑩

2. B – L violating particle & int.

12/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

What does exist as the violating interactions in the SM?

dim. 5 : 　　⇒ Leptogenesis

dim. 6 : 　 Nothing…

dim. 7 :

※ Using the SU(5) representation, [ , , ]

2013/3/20

, , , ,

, , , ,

, , ,

differential interactions ：　 mass of the SM particles 　 ⇒　 We ignore after this. using E.O.M.

𝟏𝟎 ⋅𝟓 ⋅𝟓 ⋅𝟓 ⋅𝟓h 𝟓 ⋅𝟓 ⋅𝟓⋅𝟓⋅𝟓h†

𝟏𝟎 ⋅𝟏𝟎 ⋅𝟓† ⋅𝟓† ⋅𝟓h†

𝟏𝟎 𝟓

𝟓𝟓𝟓h

𝟓

𝟓𝟓𝟓h†

𝟓

𝟓†𝟓†𝟓h†

𝟏𝟎 𝟏𝟎

2. B – L violating particle & int.

13/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Decomposition of dim. 7 interactions

These particles play a role to violate # !!

2013/3/20 2. B – L violating particle & int.

mediated

mediated a fermion

mediated a scalar bosona vector boson

★ Summary of the mediated particle scalar : , , , , fermion : , , , , , vector : , ,

⇒ number generation

14/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Decomposition of dim. 7 interaction

These particles play a role to violate # !!

2013/3/20 2. B – L violating particle & int.

mediated

mediated a fermion

mediated a scalar bosona vector boson

★ Summary of the mediated particle scalar : , , , , fermion : , , , , , vector : , ,

Focus on!

⇒ number generation

etc…

etc…

15/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Higher dimensional interaction mediated a scalar , (1)

Components (Charges are same to the SM fermions.) ,

An example :

2013/3/20

𝟏𝟎 𝟓

𝟓𝟓𝟓h𝟏𝟎

𝟏𝟎 𝟓

𝟓𝟓𝟓h

𝟓

𝑞 𝑑𝑅𝑐

𝑙𝑙h𝐷

𝟏𝟎 𝟓

𝟓𝟓𝟓h

𝑞 𝑑𝑅𝑐

𝑙𝑙h𝐷

𝐷𝑐

𝑞 𝑑𝑅𝑐

𝑙𝑙h𝐷 𝑄

h𝐷𝑙 𝑙

𝑞 𝑑𝑅𝑐

𝐸𝑐 h𝐷𝑙 𝑙

𝑞 𝑑𝑅𝑐

𝐿

2. B – L violating particle & int.

16/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Higher dimensional interaction mediated a scalar , (2)

An example of an example （ 7 dim. --> 4 dim. + 5 dim. ）

2013/3/20

𝑞 𝑑𝑅𝑐

𝑙𝑙h𝐷

𝐷𝑐

✂

■ dim. 4 :

■ dim. 5 :

𝐷𝑐

𝑞

𝑙

𝑑𝑅𝑐 †

𝑙†h𝐷†𝐷𝑐

𝐵=− 13

𝐿=−1

𝐿=+1

𝐵=− 13

generated#

+23

− 43

violating interaction!!

2. B – L violating particle & int.

17/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Higher dimensional interaction mediated a scalar , (3)

dim. 4 (3 point interactions)

dim. 5 (4 point interactions)

# generated by the decay

2013/3/20

, , , , ,

, , , , ,

, , , , ,

, , , , ,

, , ,

interaction

dim. 4

dim. 5

,

SM

SM

,

SMSM

,

2. B – L violating particle & int.

𝟏𝟎 𝟓𝟓𝟓𝟓h 𝟓

𝟓𝟓𝟓h†

𝟓𝟓†𝟓†𝟓h†

𝟏𝟎 𝟏𝟎

18/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

𝟏𝟎 𝟓𝟓𝟓𝟓h 𝟓

𝟓𝟓𝟓h†

𝟓𝟓†𝟓†𝟓h†

𝟏𝟎 𝟏𝟎 Higher dimensional interaction mediated a scalar , (3)

dim. 4 (3 point interactions)

dim. 5 (4 point interactions)

# generated by the decay

2013/3/20

, , , , ,

, , , , ,

, , , , ,

, , , , ,

, , ,

interaction

dim. 4

dim. 5

,

SM

SM

,

SMSM

,

2. B – L violating particle & int.

Sakharov’s 3 conditions

1. #B number violation It is necessary by definition.

2. C & CP violation Baryon asymmetries do not

evolve if there is no difference between particles and anti-particles.

3. Non-equilibrium condition Baryon asymmetries do not

evolve if the forward and back reaction rate is equal.

[ A. D. Sakharov (1967) ]

#B – L violating interactions(4 dim. & 5 dim. Int. with )

+The sphaleron process

19/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

𝟏𝟎 𝟓𝟓𝟓𝟓h 𝟓

𝟓𝟓𝟓h†

𝟓𝟓†𝟓†𝟓h†

𝟏𝟎 𝟏𝟎 Higher dimensional interaction mediated a scalar , (3)

dim. 4 (3 point interactions)

dim. 5 (4 point interactions)

# generated by the decay

2013/3/20

, , , , ,

, , , , ,

, , , , ,

, , , , ,

, , ,

interaction

dim. 4

dim. 5

,

SM

SM

,

SMSM

,

2. B – L violating particle & int.

Sakharov’s 3 conditions

1. #B number violation It is necessary by definition.

2. C & CP violation Baryon asymmetries do not

evolve if there is no difference between particles and anti-particles.

3. Non-equilibrium condition Baryon asymmetries do not

evolve if the forward and back reaction rate is equal.

[ A. D. Sakharov (1967) ]

#B – L violating interactions(4 dim. & 5 dim. Int. with )

+The sphaleron process

20/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary2013/3/20

Contents

2. B – L violating particle & int. 3. #B – L generation & bound

1. Introduction

2. B – L violating particles and interactions

3. B – L number generation and bound of parameter

4. Summary

aboutour

study

21/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Characteristic quantity for the generated #

the mean net number This parameter means how many # is generated by a pair of & .

　　　　

, , , , , 　　　　 : decay mode of , : branching ratio, 　 : # in the final state

# generated by the particle

　 (in case that all particles decay)

2013/3/20

𝒊 𝒍

𝒃𝒃

#：

3. #B – L generation & bound

𝒊 𝒍

𝒃𝒃

𝜖 𝑖𝑛𝑖× ×𝑛𝑖

22/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Evaluation of the mean net # (1)

　　　　　　　　 ( , : dimensionless coupling constant, 　 : cut-off scale )

2013/3/20

𝑖 (SM)

(SM) or 𝑖

(SM) (SM)¿−𝑖 𝑦 𝑖𝑎𝑏 ¿−𝑖

𝜆𝑖𝑎𝑏Λ

，

𝑖𝑎

𝑏 𝑑

𝑐𝑗

h𝐷

𝑖𝑎

𝑏×

2 body decay 3 body decaydecay width

loop function

3. #B – L generation & bound

Interference term

Trace : Taken about the SM fermion labels (a,b)

, , , ,

23/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Evaluation of the mean net # (2)

Approximation (assuming) We evaluate the trace part with only one dominant term. And we rewrite the dominant term as . Moreover, , O

2 body decay 3 body decay )⇒

★ ,

2013/3/20

𝜖 𝑖=1

256 𝜋 3

𝑚𝑖2

Λ2𝑚𝑖

16𝜋 Γ 𝑖∑𝑗

ℑ tr [𝑦 𝑖† 𝑦 𝑗 𝜆𝑖𝜆 𝑗† ]⋅ 𝑓 (𝑚 𝑗

2 /𝑚 𝑖2 )

∼ℑ 𝑦 𝑖† 𝑦 𝑗𝜆𝑖 𝜆 𝑗†

∼sin 𝛿⋅ 𝑓 (𝑚 𝑗2 /𝑚𝑖

2 )∼0.1

𝑖 𝑗

3. #B – L generation & bound

24/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Evaluation of the mean net # (2)

Approximation (assuming) Considering only dominant coupling among some , Moreover, , O

2 body decay 3 body decay ( so that, )

★ ,

2013/3/20

𝜖 𝑖=1

256 𝜋 3

𝑚𝑖2

Λ2𝑚𝑖

16𝜋 Γ 𝑖∑𝑗

ℑ tr [𝑦 𝑖† 𝑦 𝑗 𝜆𝑖𝜆 𝑗† ]⋅ 𝑓 (𝑚 𝑗

2 /𝑚 𝑖2 )

∼ℑ 𝑦 𝑖† 𝑦 𝑗𝜆𝑖 𝜆 𝑗†

∼sin 𝛿⋅ 𝑓 (𝑚 𝑗2 /𝑚𝑖

2 )∼0.1

𝑖 𝑗 Sakharov’s 3 conditions

1. #B number violation It is necessary by definition.

2. C & CP violation Baryon asymmetries do not

evolve if there is no difference between particles and anti-particles.

3. Non-equilibrium condition Baryon asymmetries do not

evolve if the forward and back reaction rate is equal.

[ A. D. Sakharov (1967) ]

#B – L violating interactions(4 dim. & 5 dim. Int. with )

+The sphaleron process

,

OAssumed

3. #B – L generation & bound

25/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Evaluation of the mean net # (2)

Approximation (assuming) Considering only dominant coupling among some , Moreover, , O

2 body decay 3 body decay ( so that, )

★ ,

2013/3/20

𝜖 𝑖=1

256 𝜋 3

𝑚𝑖2

Λ2𝑚𝑖

16𝜋 Γ 𝑖∑𝑗

ℑ tr [𝑦 𝑖† 𝑦 𝑗 𝜆𝑖𝜆 𝑗† ]⋅ 𝑓 (𝑚 𝑗

2 /𝑚 𝑖2 )

∼ℑ 𝑦 𝑖† 𝑦 𝑗𝜆𝑖 𝜆 𝑗†

∼sin 𝛿⋅ 𝑓 (𝑚 𝑗2 /𝑚𝑖

2 )∼0.1

𝑖 𝑗 Sakharov’s 3 conditions

1. #B number violation It is necessary by definition.

2. C & CP violation Baryon asymmetries do not

evolve if there is no difference between particles and anti-particles.

3. Non-equilibrium condition Baryon asymmetries do not

evolve if the forward and back reaction rate is equal.

[ A. D. Sakharov (1967) ]

#B – L violating interactions(4 dim. & 5 dim. Int. with )

+The sphaleron process

,

OAssumed

3. #B – L generation & bound

26/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Bounds for parameters

We consider about 2 situations for the violating particle species which can generate the baryon number in the Universe.

Case A : thermal produced The particle species which can generate the # is produced thermally, and after

that, it is freezed-out from the thermal bath, and then decay.

Case B : non-thermal produced + energy dominant There exists many number of the particle species which dominates the energy in

the Universe, and after that, It decays.

2013/3/20

, , , ,

3. #B – L generation & bound

Others

,

Universe

(thermally)Others

, (decoupled)

Others𝐵−𝐿𝐵−𝐿

𝐵−𝐿decay

Others

, (non-thermally produced )

?Others𝐵−𝐿

𝐵−𝐿𝐵−𝐿decay

(Many entropies are produced.)

Universe

27/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Bounds for parameters

Case A : is generated thermally

A limit to 3 point coupling constant

Using the observational value :

↓ 　2013/3/20

The transition rate from # to # by the sphaleron process[ J. A. Harvey and M. S. Turner (1990) ]

𝑛𝑖𝑠 =(𝑛𝑖𝑠 )

hot× Δ=0.278

𝑔𝑖𝑔∗× Δ

𝑛/𝑠

(𝑛𝑖𝑠 )hot

𝑛𝑖𝑠

× Δ

d.o.f. of

d.o.f. of rela. particles

(𝑛𝑠 )𝐸𝑄

𝜖 𝑖∼316𝜋 𝑦2×0.1

： the reduced ratio of from the thermal relic abundance

,

SM

SM

: entropy density

3. #B – L generation & bound

※ Generically, the relic abundance is reduced from the thermal relic.

Others

,

Others

,

Others

𝐵−𝐿𝐵−𝐿𝐵−𝐿

28/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Bounds for parameters

Case A : is generated thermally

A bound for the mass NOTE : is applicable if , pair annihilation does not happen. → 　　＠ the decay temperature of :

Other parameters In case ,

2013/3/20

𝑣× 1Γ 𝑖

𝜎 𝑖

𝑛𝑖 : the thermal averaged cross section (times the velocity) : the Plank mass （ ）

⟨𝜎 𝑖𝑣 ⟩∼ 0.01/𝑚𝑖2

What’s the value or the bound of ?

𝑦∼1.6×10−3 Δ−1 /2

・ ↓ ⇒ ↑ ⇒ ’ s lifetime becomes shorter.

・ The bound exists at which the lifetime becomes shorter than the freeze-out time scale.

3. #B – L generation & bound

( Corresponding to ※ )

𝑛𝑖×(𝜎 𝑖×𝑣 /Γ 𝑖)≲1

( : , : )

Others

,

Others

,

Others

𝐵−𝐿𝐵−𝐿𝐵−𝐿

29/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Bounds for parameters

Case A : is generated thermally

freeze-out taking into account only the scattering due to the gauge interaction (without the decay)

Boltzmann equation

Values of & when

2013/3/20

1.3 0.61 0.014 0.0022 0.00030 0.000038

1 0.99 0.89 0.47 0.10 0.017 0.0023 0.00029

𝑀𝑝=1.22×1019GeV

𝑄∗𝑄

𝐴𝜇 𝐴𝜈 ・

・ : -th modified Bessel func.

3. #B – L generation & bound

𝑚𝑖∼1014GeV

Others

,

Others

,

Others

𝐵−𝐿𝐵−𝐿𝐵−𝐿

30/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Bounds for parameters Case A : is generated thermally

　 　　　■ Boltzmann eq. with the decay

★ a lower boud exists

2013/3/20

(a)

(c)

(b)

0.10 0.017 0.0023

0.0049 0.012 0.034

�̇�𝑖+3𝐻𝑛𝑖=− ⟨ Γ 𝑖 ⟩ (𝑛𝑖−𝑛𝑖𝑒𝑞 )− ⟨𝜎 𝑖 𝑣 ⟩ (𝑛𝑖2− (𝑛𝑖𝑒𝑞 )2 )

・

3. #B – L generation & bound

𝑦∼1.6×10−3 Δ−1 /2

Others

,

Others

,

Others

𝐵−𝐿𝐵−𝐿𝐵−𝐿

31/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Bounds for parameters

Case B : ’s energy dominates in the Universe

A lot of entropies are generated by ’s decay.

We impose the additional condition ＠ as in case A　⇒　

① & ② lead to a lower mass bound :2013/3/20

,

　　 : reheating temperature by , decay

Observational value :

𝑦 3√𝑀𝑝 /𝑚𝑖∼2.2×10−6・・・①

・・・②

3. #B – L generation & bound

, Others

𝐵−𝐿𝐵−𝐿𝐵−𝐿

Others

32/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Bounds for parameters

Case B : ’s energy dominates in the Universe

Other parameters in case

These results are not so different compared with Case A.

2013/3/20 3. #B – L generation & bound

, Others

𝐵−𝐿𝐵−𝐿𝐵−𝐿

Others

33/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

, Others

𝐵−𝐿𝐵−𝐿𝐵−𝐿

Others Bound for parameters

Case B : ’s energy dominates in the Universe

Other parameters in case

These results are not so different compared with Case A.

2013/3/20

Sakharov’s 3 conditions

1. #B number violation It is necessary by definition.

2. C & CP violation Baryon asymmetries do not

evolve if there is no difference between particles and anti-particles.

3. Non-equilibrium condition Baryon asymmetries do not

evolve if the forward and back reaction rate is equal.

[ A. D. Sakharov (1967) ]

#B – L violating interactions(4 dim. & 5 dim. Int. with )

+The sphaleron process

,

OAssumed

Decay in out-of-equilibrium

* Case A : decay after freeze-out * Case B : non-thermal stateImposing

3. #B – L generation & bound

34/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

, Others

𝐵−𝐿𝐵−𝐿𝐵−𝐿

Others Bound for parameters

Case B : ’s energy dominates in the Universe

Other parameters in case

These results are not so different compared with Case A.

2013/3/20

Sakharov’s 3 conditions

1. #B number violation It is necessary by definition.

2. C & CP violation Baryon asymmetries do not

evolve if there is no difference between particles and anti-particles.

3. Non-equilibrium condition Baryon asymmetries do not

evolve if the forward and back reaction rate is equal.

[ A. D. Sakharov (1967) ]

#B – L violating interactions(4 dim. & 5 dim. Int. with )

+The sphaleron process

,

OAssumed

Decay in out-of-equilibrium

* Case A : decay after freeze-out * Case B : non-thermal stateImposing

3. #B – L generation & bound

35/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

B violating interaction --> proton decay

Rough estimation of the proton’s (partial) decay rate :

The current bound :

※ This is because the B violating interaction comes from dim.7 operator.

2013/3/20

⟨h0 ⟩𝑢𝑢𝑅𝑐

𝑢

𝑑𝑅𝑐

𝑑𝑅𝑐

𝜈𝐿

𝑝

𝜋+¿¿

𝑄

enough stable!Saying exactly, this interaction is not

sizable for the proton decay.

3. #B – L generation & bound

36/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary2013/3/20 3. #B – L generation & bound 4. Summary

Contents

1. Introduction

2. B – L violating particles and interactions

3. B – L number generation and bound of parameter

4. Summary

aboutour

study

37/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Summary

We have shown the new scenario generating which was obtained from dim. 7 interactions in SM.

The particles with the violating interactions are in the representation of , , , which are scalar bosons, , , , , which are fermions, , which are vector bosons of ,

In particular, we have focused on the bosons of and (components : , , , , ), and we have shown the concrete interactions.

We have evaluated the mean net # by the decay of , , , , , and then we have limited to some parameters (yukawa couplings, masses, or so) with some approximation and the observational #.

Case A : thermal produced, , 　

Case B : non-thermal + energy dominant, ( ⇔ )

2013/3/20 4. Summary

38/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

back up

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39/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

2013/3/20

40/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Sakharov’s 3 conditions

1. #B number violation It is necessary by the definition.

2. C & CP violation Baryon asymmetries do not

evolve if there is no difference between particles and anti-particles.

3. Non-equilibrium condition Baryon asymmetries do not

evolve if the forward and back reaction rate is equal.

2013/3/20

[ A. D. Sakharov (1967) ]

b

bX

1. Introduction

These are needed to be evolved from to of the Universe.

𝑋 𝑏 ,𝑏𝑏 , 𝑙

𝐵=+2/3𝐵=−1/3

41/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Sakharov’s 3 conditions

1. #B number violation It is necessary by definition.

2. C & CP violation Baryon asymmetries do not

evolve if there is no difference between particles and anti-particles.

3. Non-equilibrium condition Baryon asymmetries do not

evolve if the forward and back reaction rate is equal.

2013/3/20

[ A. D. Sakharov (1967) ]

b

bb𝑋

l𝑋

𝐵=+2/3

𝐵=−1/3

+1/3

𝑋 𝑏 ,𝑏𝑏 , 𝑙

+1/3

0 −1 /3

Conditions to be evolved from to of the Universe.

1. Introduction

42/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Sakharov の 3 条件

1. バリオン数の破れ 定義から必要

2. C & CP の破れ 粒子・反粒子の反応に差がな

ければバリオン非対称性は発展しない

3. 非平衡反応 反応と逆反応が同じ速さで進

むとバリオン非対称性は発展しない

2013/3/20

[ A. D. Sakharov (1967) ]

𝒃

b b

𝑋𝒍

𝐵=+2/3𝐵=−1/3

+1/3

𝑋 𝑏 ,𝑏𝑏 , 𝑙

+1/3

0 −1 /3

の宇宙から でない宇宙に発展するための条件

1. Introduction

43/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

dim. 7 相互作用項の分解

2013/3/20

𝟓

𝟓𝟓𝟓h†

𝟓

𝟓†𝟓†𝟓h†

𝟏𝟎 𝟏𝟎

スカラーボソン： , 　フェルミオン： , ベクトルボソン： ,

スカラーボソン： , , , , , 　フェルミオン： , , , , ベクトルボソン： , , , , ,

スカラー，ベクトル： , , , , , 　フェルミオン： , , , , , ,

44/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Decomposition of dim. 7 interaction (1)

1.

2013/3/20

𝟏𝟎 𝟓

𝟓𝟓𝟓h

𝟏𝟎 𝟓

𝟓𝟓𝟓h

𝟏𝟎 𝟓

𝟓𝟓𝟓h

𝟏𝟎 𝟓

𝟓𝟓𝟓h

𝟏𝟎 𝟓

𝟓𝟓𝟓h

𝟏𝟎 𝟓

𝟓𝟓𝟓h

𝟏𝟎 𝟓

𝟓𝟓𝟓h

𝟏𝟎 𝟓

𝟓𝟓𝟓h

𝟏𝟎 𝟓

𝟓𝟓𝟓h

𝟏𝟎 𝟓

𝟓𝟓𝟓h

𝟏𝟎 𝟓

𝟓𝟓𝟓h

mediated a scalar boson ： , , , ,

mediated a fermion ： , , , , mediated a vector boson ： , , , ,

,

,

,

,

, ,

,

,

, ,

𝝏 𝝏

𝝏 𝝏

𝝏 𝝏𝝏

𝝏

2. B – L violating particle & int.

45/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary2013/3/20

𝟓

𝟓𝟓𝟓h†

𝟓

𝟓†𝟓†𝟓h†

𝟏𝟎 𝟏𝟎

： ,

scalar, vector : , , , , , 　 fermion : , , , , , ,

: , , , , ,

2. B – L violating particle & int.

Decomposition of dim. 7 interaction (2)

2. scalar boson, fermion,　　　　 vector boson

3. scalar boson,vector boson

fermion : , , , ,

★ Summary of the mediated particle

These particles play a role to violate # !!

46/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary2013/3/20

𝟓

𝟓𝟓𝟓h†

𝟓

𝟓†𝟓†𝟓h†

𝟏𝟎 𝟏𝟎

： ,

scalar, vector : , , , , , 　 fermion : , , , , , ,

: , , , , ,

2. B – L violating particle & int.

Decomposition of dim. 7 interaction (2)

2. scalar boson, fermion,　　　　 vector boson

3. scalar boson,vector boson

fermion : , , , ,

★ Summary of the mediated particle

These particles play a role to violate # !! ⇒ number generation

etc…

etc…

Focus on!

47/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Decomposition of dim. 7 interaction (1)

2013/3/20 2. B – L violating particle & int.

𝟏𝟎 𝟓

𝟓𝟓𝟓h

𝟏𝟎 𝟓

𝟓𝟓𝟓h

,

𝟏𝟎 𝟓

𝟓𝟓𝟓h,

𝟏𝟎 𝟓

𝟓𝟓𝟓h,

𝟏𝟎 𝟓

𝟓𝟓𝟓h,

𝟓

𝟓𝟓𝟓h†

𝟓

𝟓 𝟓

𝟓𝟓𝟓h†

𝟏𝟎

𝟓 𝟓

𝟓𝟓𝟏𝟎𝟓h†

𝟓†𝟓†𝟓h†

𝟏𝟎 𝟏𝟎

𝟏𝟎 𝟏𝟎

𝟓𝟓𝟓h†𝟏𝟎

𝟏𝟎 𝟏𝟎

𝟓†𝟓†, 𝟓h†

mediated a fermion

mediated a scalar boson

48/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Decomposition of dim. 7 interaction (1)

2013/3/20 2. B – L violating particle & int.

𝟓

𝟓𝟓𝟓h†

𝟓

𝟓 𝟓

𝟓𝟓𝟓h†

𝟏𝟎

𝟓 𝟓

𝟓𝟓𝟏𝟎𝟓h†

𝟓†𝟓†𝟓h†

𝟏𝟎 𝟏𝟎

𝟏𝟎 𝟏𝟎

𝟓𝟓𝟓h†𝟏𝟎

𝟏𝟎 𝟏𝟎

𝟓†𝟓†, 𝟓h†

𝟏𝟎 𝟏𝟎

𝟓𝟓𝟓h†,

𝟏𝟎 𝟏𝟎

𝟓†𝟓†, 𝟓h†

𝟏𝟎 𝟏𝟎

𝟓𝟓𝟓h†

,

mediated a vector boson

mediated a fermion

mediated a scalar boson

49/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Decomposition of dim. 7 interaction (1)

2013/3/20 2. B – L violating particle & int.

𝟏𝟎 𝟓

𝟓𝟓𝟓h

𝟏𝟎 𝟓

𝟓𝟓𝟓h

,

𝟏𝟎 𝟓

𝟓𝟓𝟓h,

𝟏𝟎 𝟓

𝟓𝟓𝟓h,

𝟏𝟎 𝟓

𝟓𝟓𝟓h,

𝟓

𝟓𝟓𝟓h†

𝟓

𝟓 𝟓

𝟓𝟓𝟓h†

𝟏𝟎

𝟓 𝟓

𝟓𝟓𝟏𝟎𝟓h†

𝟓†𝟓†𝟓h†

𝟏𝟎 𝟏𝟎

𝟏𝟎 𝟏𝟎

𝟓𝟓𝟓h†𝟏𝟎

𝟏𝟎 𝟏𝟎

𝟓†𝟓†, 𝟓h†

50/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

スカラー , を媒介する高次相互作用

,

2013/3/20

𝟏𝟎 𝟓

𝟓𝟓𝟓h𝟏𝟎

𝟏𝟎 𝟓

𝟓𝟓𝟓h

𝟓

𝟓 𝟓

𝟓𝟓𝟓h†

𝟏𝟎

𝑞 𝑑𝑅𝑐

𝑙𝑙h𝐷

51/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary2013/3/20

𝟏𝟎 𝟓

𝟓𝟓𝟓h

𝟓

𝟓𝟓𝟓h†

𝟓

𝟓†𝟓†𝟓h†

𝟏𝟎 𝟏𝟎

𝟏𝟎 𝟓

𝟓𝟓𝟓h

52/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

Summary1. どのような粒子や相互作用が B – L 数を破りうるかを論じた。

そのような粒子や相互作用を模索するために，標準模型内の粒子で組める高次元相互作用項に着目した。

B – L 数を破る高次元相互作用項は， 5 次に 1 種類，７次に 11 種類存在する。

7 次の相互作用項を 2 つに分解することで， B – L 数を破りうる粒子にどのようなものがあるかを挙げた。

2. 観測的な制限などから， B – L 数を破る粒子の質量や結合定数などに制限を与えた。 B – L 数を破りうる粒子として，我々の研究では特に SU(5) での

10 表現と 5 表現に属するものに注目し、それらが生成する B – L 数を評価した。

観測的な制限から、それらに含まれるパラメータ，特に質量に対して制限を与えた。

2013/3/20 4. Summary

53/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

1. Introduction

2. B – L 数を破る粒子と相互作用

3. B – L 数生成とパラメータ制限

4. Summary

2013/3/20

Contents

1. Introduction

我々が行った研究について

54/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

1. Introduction

2. B – L 数を破る粒子と相互作用

3. B – L 数生成とパラメータ制限

4. Summary

2013/3/20

Contents

1. Introduction 2. B – L violating particle & int.

我々が行った研究について

55/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

1. Introduction

2. B – L 数を破る粒子と相互作用

3. B – L 数生成とパラメータ制限

4. Summary

2013/3/20

Contents

2. B – L violating particle & int. 3. #B – L creation & limit

我々が行った研究について

56/341. Introduction 2. B – L violating particle & int. 3. #B – L generation & bound 4. Summary

1. Introduction

2. B – L 数を破る粒子と相互作用

3. B – L 数生成とパラメータ制限

4. Summary

2013/3/20

Contents

3. #B – L creation & limit 4. Summary

我々が行った研究について