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Baryogenesis by B - L g eneration 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.). The IOPAS HEP Theory Journal Club ＠ Academia Sinica. Introduction - PowerPoint PPT Presentation
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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
