Baryogenesis: finding the origin of baryons (or leptons) present in the universe

20160219 Sangwon Ma

The table of contents

• Introduction

• Baryogenesis Models

I. Electroweak baryogenesis in the standard model

I. Background, Sakharov condition

The beginning

• Introduction

I. Background, Sakharov condition

• Baryogenesis Models

I. Electroweak baryogenesis in the standard model

What are baryons?

Baryon: a type of composite particle which contains an odd number of valence quarks (except for only 1 quark)

Fermions

Characters

• participate in strong, weak, electromagnetic

and gravity interaction

• fermion (described by F-D statistics)

• hadron (composite of valence quarks)

• Almost all visible matter in the universe is

made up of baryons

• There are 120 types of baryons

Ex) 𝑝, 𝑛, Σ±, Σ0, Ξ−, Ξ0, Ω− …

What are baryons?

Baryon: a type of composite particle which contains an odd number of valence quarks (except for only 1 quark)

Fermions

Characters

• participate in strong, weak, electromagnetic

and gravity interaction

• fermion (described by F-D statistics)

• hadron (composite of valence quarks)

• Almost all visible matter in the universe is

made up of baryons

• There are 120 types of baryons

Ex) 𝑝, 𝑛, Σ±, Σ0, Ξ−, Ξ0, Ω− …

Who has seen a natural antimatter object?

A few antiprotons and positrons less than 1% of the cosmic rays are not

relic antimatter, just made by high energy process around pulsar etc…

Serpico, P. D. (December 2012). "Astrophysical models for the origin of the positron "excess"". Astroparticle Physics. 39-40: 2–11

If antimatter-dominated regions exist, the gamma rays produced

along the boundary would be detectable. (~100 MeV/reaction)

Sather, E. (Spring 1999).“The Mystery of the Matter Asymmetry”.Beam Line. 26 (1): 31

If domains of antimatter exist, they are separated larger than Virgo

cluster (~10 Mpc).

Antonio, R. (February 2008).“Theories of Baryogenesis”.[hep-ph]/9807454

No one

It is reasonable to consider the universe consisting of matter.

How much particles are there?

𝐵, 𝐿 : additive quantum numbers that count baryons and leptons, respectively.

𝐵 =1

3(𝑛𝑞 − 𝑛 ത𝑞) 𝐿 = 𝑛𝑙 − 𝑛 ҧ𝑙

(quark) 𝑢, 𝑑, 𝑠, 𝑐, 𝑏, 𝑡 : 𝐵 =1

3

(lepton) 𝑒−, 𝜈𝑒 , 𝜇−, 𝜈𝜇, 𝜏

−, 𝜈𝜏 : 𝐿 = 1

(anti-quark) ത𝑢, ҧ𝑑, ҧ𝑠, ҧ𝑐, ത𝑏, ҧ𝑡 : 𝐵 = −1

3(anti-lepton) 𝑒+, ഥ𝜈𝑒 , 𝜇

+, 𝜈𝜇, 𝜏+, ഥ𝜈𝜏: 𝐿 = −1

Baryon and Lepton number are used

Physics seems to conserve 𝐵 and 𝐿

The baryon and lepton number in all reactions we have been observed were conserved so far.

[1] Bartlomiej, R. (July 2016) “Search for baryon and lepton number violation in heavy baryon decays and the background studies for exotic searches”, CERN-THESIS-2016-118

[1]

𝐵,𝐻𝑆𝑀 ≃ 0

𝐿, 𝐻𝑆𝑀 ≃ 0(accidental global symmetry in SM)

[2] Jonathan M. A. (May 2014) “Baryon and lepton numbers in particle physics beyond the standard model”, INSPIRE-1322995

[2]

𝐵 − 𝐿, 𝐻𝑆𝑀 ≡ 0 (exact global symmetry in SM)

[3] Uwe-Jens W. (February 19, 2018) “The Standard Model of Particle Physics”, p.116 - 118

[3]

Baryon asymmetry in the universe

𝜂𝛾 ≡𝑛𝑏 − 𝑛ത𝑏𝑛𝛾

=

Ω𝑏𝑚𝑏

𝜌𝑐

20.3𝑇01𝐾

3

cm−3

≈ 6 × 10−101)

𝜂𝑠 ≡𝑛𝑏 − 𝑛 ത𝑏

𝑠=

Ω𝑏𝑚𝑏

𝜌𝑐

2𝜋2

45σboson𝑔𝑖𝑇𝑖

3 +78σfermion𝑔𝑗𝑇𝑗

3≃ 0.861 × 10−102)

𝑛𝑏 , 𝑛ത𝑏 ∝ 𝑎 𝑡 −3 ∝ 𝑇3 and 𝑎(𝑡)3𝑠 ∝ 𝑎 𝑡 3𝑇3 ≃ 𝑐𝑜𝑛𝑠𝑡.

Planck result (2018) → 𝑇0, 𝐻0, Ω𝐵ℎ

2Big Bang nucleosynthesis→ 𝑛𝑛(𝑡): 𝑛𝑝(𝑡)

Baryonic asymmetry (𝐵 > 0) is initial condition?

Initial asymmetry

𝜂𝑠0 =𝑛𝑏0 − 𝑛𝑏0

𝑠0

Inflation (~60 e-folds)

Intermediate asymmetry

𝜂𝑠1 =𝑛𝑏0 − 𝑛 ത𝑏0 × 𝑒−3∙60

𝑠0 × 𝑒−3∙60

Reheating Final asymmetry

𝜂𝑠2 =𝑛𝑏0 − 𝑛 ത𝑏0 × 𝑒−3∙60

𝑠0

Initial baryon asymmetry is washed out by inflation

[2] Lars B., Ariel G. (2004) “Cosmology and Particle Astrophysics”, Springer, p.180-181

[1] I. Baldes, Early universe cosmology and the matter-antimatter asymmetry, Ph.D. thesis (2015).

[2]

[1]

Baryonic asymmetry (𝐵 > 0) is semi-initial condition

[1] I. Baldes, Early universe cosmology and the matter-antimatter asymmetry, Ph.D. thesis (2015).

Inflation start~10−36s

Inflation end~10−32s

nucleosynthesis10s~20min

Baryogenesis, Leptogenesis[1]

𝑡

𝜂𝑠~0𝜂𝑠~? 𝜂𝑠~0.86 × 10−10

Baryogenesis: the hypothetical process that took place during the early universe that produced matter-antimatter asymmetry

Sakharov condition (necessary condition)

𝐵 = 0 state 𝐵 > 0 state

‘some reaction’

𝜓𝑖 𝐵 𝜓𝑖 = 𝐵0 𝜓𝑓 𝐵 𝜓𝑓 = 𝐵1 > 𝐵0

𝐵 symmetry violation

Some reaction

Sakharov condition (necessary condition)

𝐵 = 0 state 𝐵 > 0 state

‘some reaction’

𝜓𝑖 𝐵 𝜓𝑖 = 𝐵0 𝜓𝑓 𝐵 𝜓𝑓 = 𝐵1 > 𝐵0

𝐵 symmetry violation

However if 𝐶 symmetry holds,

𝜓𝑖 𝐵 𝜓𝑖 = −𝐵0 𝜓𝑓 𝐵 𝜓𝑓 = −𝐵1 < −𝐵0

𝜓𝑖 𝐵 𝜓𝑖 = +𝐵0 𝜓𝑓 𝐵 𝜓𝑓 = +𝐵1 > +𝐵0

Since 𝑃 𝜓𝑖 → 𝜓𝑓 = 𝑃 𝜓𝑖 → 𝜓𝑓 , ∆𝐵 = 0

Some reaction

“𝐶 symmetry must be violated”

Sakharov condition (necessary condition)

𝐵 = 0 state 𝐵 > 0 state

‘some reaction’

Still if 𝐶𝑃 symmetry (𝑇 invariance) holds,

𝜓𝑖(𝒓𝑖 , 𝒑𝑖 , 𝒔𝑖) 𝐵 𝜓𝑖(𝒓𝑖 , 𝒑𝑖 , 𝒔𝑖)= 𝐵0

𝜓𝑓(𝒓𝑓, 𝒑𝑓, 𝒔𝑓) 𝐵 𝜓𝑓(𝒓𝑓, 𝒑𝑓, 𝒔𝑓)

= 𝐵1 > 𝐵0

𝜓𝑓(𝒓𝑓, −𝒑𝑓 , −𝒔𝑓) 𝐵 𝜓𝑓(𝒓𝑓, −𝒑𝑓, −𝒔𝑓)

= 𝐵0

𝜓𝑖(𝒓𝑖 , −𝒑𝑖 , −𝒔𝑖) 𝐵 𝜓𝑖(𝒓𝑖 , −𝒑𝑖 , −𝒔𝑖)= 𝐵1 > 𝐵0

Sakharov condition (necessary condition)

𝐵 = 0 state 𝐵 > 0 state

‘some reaction’

But if 𝐶𝑃 symmetry (𝑇 invariance) holds,

𝜓𝑖(𝒓𝑖 , 𝒑𝑖 , 𝒔𝑖) 𝐵 𝜓𝑖(𝒓𝑖 , 𝒑𝑖 , 𝒔𝑖)= 𝐵0

𝜓𝑓(𝒓𝑓, 𝒑𝑓, 𝒔𝑓) 𝐵 𝜓𝑓(𝒓𝑓, 𝒑𝑓, 𝒔𝑓)

= 𝐵1 > 𝐵0

𝜓𝑓(𝒓𝑓, −𝒑𝑓 , −𝒔𝑓) 𝐵 𝜓𝑓(𝒓𝑓, −𝒑𝑓, −𝒔𝑓)

= 𝐵0

𝜓𝑖(𝒓𝑖 , −𝒑𝑖 , −𝒔𝑖) 𝐵 𝜓𝑖(𝒓𝑖 , −𝒑𝑖 , −𝒔𝑖)= 𝐵1 > 𝐵0

ඵ∆𝐵(𝑟, 𝒑, 𝒔) 𝑑𝒑𝑑𝒔 = 0“𝐶𝑃 symmetry must be violated”

Sakharov condition (necessary condition)

𝐵 = 0 state 𝐵 > 0 state

‘some reaction’

Finally if the universe was in thermal equilibrium,

𝐵 = Tr 𝑒−𝛽𝐻𝐵 = Tr 𝐶𝑃𝑇 𝐶𝑃𝑇 −1𝑒−𝛽𝐻𝐵 = Tr 𝑒−𝛽𝐻 𝐶𝑃𝑇 𝐶𝑃𝑇 −1𝐵 = Tr 𝑒∗𝛽𝐻 𝐶𝑃𝑇 𝐵 𝐶𝑃𝑇 −1 = Tr 𝑒−𝛽𝐻(−𝐵) = − 𝐵

Sakharov condition (necessary condition)

𝐵 = 0 state 𝐵 > 0 state

‘some reaction’

Finally if the universe was in thermal equilibrium,

𝐵 = Tr 𝑒−𝛽𝐻𝐵 = Tr 𝐶𝑃𝑇 𝐶𝑃𝑇 −1𝑒−𝛽𝐻𝐵 = Tr 𝑒−𝛽𝐻 𝐶𝑃𝑇 𝐶𝑃𝑇 −1𝐵 = Tr 𝑒∗𝛽𝐻 𝐶𝑃𝑇 𝐵 𝐶𝑃𝑇 −1 = Tr 𝑒−𝛽𝐻(−𝐵) = − 𝐵

According to statistical physics, 𝑃𝜓=𝜓𝑖= 𝑃𝜓=𝜓𝑖

𝐻𝑖

From 𝑋 ത𝑋 → 𝛾𝛾 and 𝜇𝑋 + 𝜇 ത𝑋 = 2𝜇𝛾 = 0,

𝜇𝑋 = −𝜇 ത𝑋

𝐻𝑖 = 𝐻𝑖(𝑝𝑖 , 𝑉𝑖 , 𝑚𝑖 , 𝜇𝑖 , … )

From Dirac equation, 𝑚𝑋 = 𝑚 ത𝑋

By 𝐵 violation, 𝑋𝑋 → ത𝑋 ത𝑋 etc…

𝜇𝑋 = 𝜇 ത𝑋 = 0

𝐻𝑖 = 𝐻 ҧ𝑖

Sakharov condition (necessary condition)

𝐵 = 0 state 𝐵 > 0 state

‘some reaction’

Finally if the universe was in thermal equilibrium,

𝐵

න𝐵 𝒓 𝑑𝒓 = 0

The microscopic asymmetry may be generated, but it is macroscopically symmetric in the thermal equilibrium.

“The reaction must be out of thermal equilibrium”

Sakharov 3 condition (necessary condition)

Baryon number violation

𝐶 and 𝐶𝑃 violation

Departure from thermal equilibrium

“Baryogenesis must satisfy these 3 condition”

The Next contents

• Introduction

• Baryogenesis Models

I. Electroweak baryogenesis in the standard model

I. Background, Sakharov condition

History of baryogenesis

James M. Cline, (2006) “Baryogenesis”, arXiv:hep-ph/0609145

20031965

Baryogenesis models• Electroweak Baryogenesis• Thermal Leptogenesis• GUT Baryogenesis• Affleck-Dine Baryogenesis• Spontaneous Baryogenesis• Primordial Cosmic Strings Baryogenesis• Primordial Magnetic Fields Baryogenesis• Primordial Black Holes Baryogenesis• Dissipative Baryogenesis• Warm Baryogenesis• Cold Baryogenesis• Cloistered Baryogenesis• Planck Baryogenesis• Post-Sphaleron Baryogenesis• WIMPy Baryogenesis• Dirac Leptogenesis• Resonant Leptogenesis• Non-Local Electroweak Baryogeneis• Magnetic-Assisted EW Baryogenesis• Singlet-Assisted EW Baryogenesis• Varying Constants Driven Baryogenesis

Baryogenesis models• Electroweak Baryogenesis• Thermal Leptogenesis• GUT Baryogenesis• Affleck-Dine Baryogenesis• Spontaneous Baryogenesis• Primordial Cosmic Strings Baryogenesis• Primordial Magnetic Fields Baryogenesis• Primordial Black Holes Baryogenesis• Dissipative Baryogenesis• Warm Baryogenesis• Cold Baryogenesis• Cloistered Baryogenesis• Planck Baryogenesis• Post-Sphaleron Baryogenesis• WIMPy Baryogenesis• Dirac Leptogenesis• Resonant Leptogenesis• Non-Local Electroweak Baryogeneis• Magnetic-Assisted EW Baryogenesis• Singlet-Assisted EW Baryogenesis• Varying Constants Driven Baryogenesis

described in my report

Electroweak Baryogenesis in the standard modelThe universe temperature 𝑇 ≳ 100GeV

The standard model expects that the early universe enough after inflation has the symmetry of

𝑆𝑈 3 𝐶 × 𝑆𝑈 2 𝐿 × 𝑈 1 𝑌

Electroweak BaryogenesisThe universe temperature 𝑇~100GeV

But as the universe cools down to ~100GeV, the Higgs field acquires a nonzero vacuum expectation value followed by the spontaneous symmetry breaking

𝑆𝑈 3 𝐶 × 𝑆𝑈 2 𝐿 × 𝑈 1 𝑌 → 𝑆𝑈 3 𝐶 × 𝑈 1 EM

𝜙 = 0 → 𝜙 > 0

Electroweak Baryogenesis𝑇~100GeV

𝜙 = 0

𝜙 > 0

𝜙 = 0

𝜙 > 0

𝜙 > 0

𝜙 > 0

𝜙 = 0

𝜙 = 0

Bubbles of broken phase are created

Electroweak Baryogenesis

𝑣 = 𝜑(𝑇)

Electroweak Baryogenesis𝑇~100GeV

𝜙 = 0

𝜙 > 0

𝜙 = 0

𝜙 > 0

𝜙 > 0

𝜙 > 0

𝜙 = 0

𝜙 = 0

There exist the domain walls if the electroweak phase transition is 1st-order

③ Departure from thermal equilibrium

Electroweak Baryogenesis𝑇~100GeV

𝜙 > 0 bubble𝜙 = 0 space

𝑄𝛼,𝑅 𝑄𝛼,𝐿

Particles interact with Higgs field at the domain wall by scattering

𝑇(𝑄𝛼,𝑅) 𝑇(𝑄𝛼,𝐿)

𝑅(𝑄𝛼,𝑅) 𝑅(𝑄𝛼,𝐿)

Electroweak Baryogenesis𝑇~100GeV

𝜙 > 0 bubble𝜙 = 0 space

𝑄𝛼,𝑅 𝑄𝛼,𝐿

Particles interact with Higgs field at the domain wall by scattering

𝑇(𝑄𝛼,𝑅)

𝑅(𝑄𝛼,𝑅)

𝑇(𝑄𝛼,𝐿)

𝑅(𝑄𝛼,𝐿)

𝑇 𝑄𝛼,𝑅 > 𝑇(𝑄𝛼,𝐿)

② C, CP violation

𝑇 𝑄𝛼,𝑅 + 𝑇 𝑄𝛼,𝐿 ≠ 𝑇 𝑄𝛼,𝑅 + 𝑇(𝑄𝛼,𝐿)

Electroweak Baryogenesis𝑇~100GeV

𝜙 > 0 bubble𝜙 = 0 space

There exist quark and corresponding anti-quark net flux passing through the domain wall.

Particle

Anti-particle

Sphalerons

Sphalerons

A static field configuration solution of the equations of motion in the electroweak theory whose gauge group is 𝑆𝑈(2) × 𝑈(1) and Higgs field is a complex doublet.

[1] F. R. Klinkhamer and N. S. Manton, “A saddle-point solution in the Weinberg-Salam theory”, Phys. Rev. D30, 2212 (1984)

[1]

Sphalerons

The energy functional iswhere

R. F. Klinkhamer and N. S. Manton, Phys. Rev. D30, 2212 (1984)

Sphalerons

The field equations arewhere

The energy functional iswhere

R. F. Klinkhamer and N. S. Manton, Phys. Rev. D30, 2212 (1984)

Sphalerons

Assuming that 𝑔′ = 0, the solution of the field equations is

The field equations arewhere

The energy functional iswhere

where

R. F. Klinkhamer and N. S. Manton, Phys. Rev. D30, 2212 (1984)

Properties of sphalerons

• Corresponding to saddle points of the energy functional → unstable

• Being static and localized in space → particle-like

• Identified with the configuration of maximum energy on some noncontractible loop

• The Chern-Simons number of the sphaleron is 𝑁𝐶𝑆 sphaleron =1

2

• Sphaleron has a classical magnetic dipole moment along the axis of symmetry

• Violating 𝐵 + 𝐿, preserving 𝐵 − 𝐿

• It has baryon number 𝐵 =1

2and lepton number 𝐿 =

1

2

Properties of sphalerons

• Corresponding to saddle points of the energy functional → unstable

• Being static and localized in space → particle-like

• Identified with the configuration of maximum energy on some noncontractible loop

• The Chern-Simons number of the sphaleron is 𝑁𝐶𝑆 sphaleron =1

2

• Sphaleron has a classical magnetic dipole moment along the axis of symmetry

• Violating 𝐵 + 𝐿, preserving 𝐵 − 𝐿

• It has baryon number 𝐵 =1

2and lepton number 𝐿 =

1

2

Properties of sphalerons

interior

new vacuum

exterior

original vacuum

Field configuration space

A sphaleronEnergy

Vacuum performs a transition from unbroken phase to broken phase at the domain wall

Sphaleron is a static point of process connecting two vacua whose 𝑁𝐶𝑆,0, 𝑁𝐶𝑆,0 ± 1

A. Riotto, “Theories of baryogenesis”, arXiv:hep-ph/9807454 (1998)

Properties of sphalerons

If a system performs a transition, ℊ𝑣𝑎𝑐𝑛

= ⋯ ,𝑁𝐶𝑆 = 𝑛 → ℊ𝑣𝑎𝑐𝑚

= ⋯ ,𝑁𝐶𝑆 = 𝑚 ,

sphalerons generate a baryonic asymmetry by

∆𝐵 =1

2∆ 𝐵 + 𝐿 + ∆ 𝐵 − 𝐿 = 𝑁𝑓∆𝑁𝐶𝑆

𝑁𝑓 = 3 : number of fermionic families in SM

𝑁𝐶𝑆 =𝑔22

32𝜋2න𝑑3𝑥𝜖𝑖𝑗𝑘Tr 𝐴𝑖𝜕𝑗𝐴𝑘 +

2

3𝑖𝑔2𝐴𝑖𝐴𝑗𝐴𝑘

∆𝑁𝐶𝑆= 𝑚 − 𝑛 = 0,±1,±2, ±3⋯A. Riotto, “Theories of baryogenesis”, arXiv:hep-ph/9807454 (1998)

① B violation

that is, 𝑄 → ത𝐿 or ത𝑄 → 𝐿

Properties of sphalerons

The sphaleron process rates in broken phase and unbroken phase are different

Γbrokensp

∝ exp(−𝑆sp

𝑇) < Γunbroken

sp∝ 𝛼𝑊𝑇

4

( The calculation is very complicated… )

A. Riotto, “Theories of baryogenesis”, arXiv:hep-ph/9807454 (1998)

Broken phase inside a bubble Unbroken phase outside a bubble

Sphaleron process : ത𝑄 → 𝐿

Sphaleron process : Q → ത𝐿 (less)

(much)

Baryon asymmetry may be generated around the domain wall

𝑇~100GeVElectroweak Baryogenesis

Unbroken phase outside a bubble

𝑇~100GeV

Bubbles expand

Electroweak Baryogenesis

Broken phase inside a bubble

Electroweak Baryogenesis

Broken phase that we observe today

Baryon asymmetry is generated

𝑇 ≲ 100GeV

Problems of Electroweak Baryogenesis in the standard model

The standard model predicts that the electroweak phase transition become 1st-order if 𝑚𝐻 ≲ 88GeV. (The upper bound may be changed depending on which analytic method you use)

→ However 𝑚𝐻 = 125GeV is confirmed in LHC.

The CP violation sufficient to generate the baryon asymmetry 𝜂𝑠 ≃ 0.861 × 10−10 is 𝛿𝐶𝑃 ≳ 10−3 at the early universe.

→ But the SM predicts that 𝛿𝐶𝑃 ≃ 10−20 at the early universe.

A. Riotto, “Theories of baryogenesis”, arXiv:hep-ph/9807454 (1998)

Other version of Electroweak Baryogenesis

• Electroweak baryogenesis in the minimal supersymmetric standard model

• Electroweak baryogenesis in the 𝜙6 model

• ‘Cold’ electroweak baryogenesis in the standard model

• Electroweak baryogenesis in the two doublet and inert singlet extension of the standard model

• Electroweak baryogenesis above + neutral Majorana fermion 𝜒

Bibliography

1. I. Baldes, “Early universe cosmology and the matter-antimatter asymmetry”, Ph.D. thesis (2015)

2. A. Long, “The matter – antimatter asymmetry of the universe and baryogenesis” (2017)

3. R. Kolb, “Standard model & Baryogenesis at 50 years” (2017)

4. A. Riotto, “Theories of baryogenesis”, arXiv:hep-ph/9807454 (1998)

5. M. Trodden, “Baryogenesis and leptogenesis”, arXiv:hep-ph/0411301 (2004)

6. C. Balazs, “Baryogenesis: A small review of the big picture”, arXiv:1411.3398 (2014)

7. R. F. Klinkhamer and N. S. Manton, “A saddle-point solution in the Weinberg-Salam theory”, Phys. Rev. D30, 2212 (1984)

8. James M. Cline, “Baryogenesis”, arXiv:hep-ph/0609145 (2006)

9. L. Bergstrom, A. Goobar, “Cosmology and Particle Astrophysics”, Springer (2004)

I found the typo in my report while I study the electroweak baryogenesis again.

𝐵𝑇= Tr 𝑒−𝛽𝐻 𝐵 = Tr 𝐶𝑃𝑇−1𝐶𝑃𝑇𝑒−𝛽𝐻 𝐵

≠ Tr 𝑒−𝛽𝐻𝐶𝑃𝑇−1 𝐵𝐶𝑃𝑇 = − 𝐵𝑇

( There might be more typos … )