Particle Physics and Cosmology Baryon asymmetry.

Particle PhysicsParticle Physicsand Cosmologyand Cosmology

Baryon asymmetryBaryon asymmetry

Boltzmann equation in Boltzmann equation in terms of terms of

cross sectioncross section

..

dimensionless inverse dimensionless inverse temperaturetemperature

dimensionlessdimensionlesstime variable time variable in units ofin units ofparticle mass m particle mass m

m : particle massm : particle mass

small x : particle is relativistic x<3small x : particle is relativistic x<3large x : particle is non-relativistic x>3large x : particle is non-relativistic x>3

particle number per particle number per entropyentropy

cold relic fractioncold relic fraction

not necessarily order one !not necessarily order one !

cold relic abundance ,cold relic abundance ,mass and cross sectionmass and cross section

mm(m,(m,σσ

AA))

inversely proportional to cross section ,inversely proportional to cross section , plus logarithmic dependence of xplus logarithmic dependence of xff

baryon relics in baryon relics in baryon symmetric Universebaryon symmetric Universe

observed : Y = observed : Y = ηη ≈ 10 ≈ 10 -10-10

ΩΩbb = 0.045 = 0.045

baryons :

the matter of stars and humans

A.CocA.Coc

Abundancies of Abundancies of primordialprimordiallight elementslight elementsfrom from nucleosynthesisnucleosynthesis

primordial abundances primordial abundances for three GUT modelsfor three GUT models

T.Dent,T.Dent,S.Stern,…S.Stern,…

present present observatioobservations : 1ns : 1σσ

HeHe

DD

LiLi

present baryon number present baryon number

anti-baryons in anti-baryons in baryon asymmetric baryon asymmetric

UniverseUniverse

conserved baryon conserved baryon asymmetryasymmetry

no baryon number violating processes inno baryon number violating processes instandard model of particle physics at energystandard model of particle physics at energybelow 1 GeVbelow 1 GeV

baryon asymmetry must exist at T = 1 GeV baryon asymmetry must exist at T = 1 GeV

high temperature baryon high temperature baryon problemproblem

baryon number violation in baryon number violation in standard modelstandard model

baryon number is global symmetry of baryon number is global symmetry of interactions in the standard modelinteractions in the standard model

violated by quantum anomaly violated by quantum anomaly ( no ( no anomalies possible for local symmetries : anomalies possible for local symmetries : corresponding charge , like electric corresponding charge , like electric charge , exactly conserved )charge , exactly conserved )

sphaleron processes generate strong sphaleron processes generate strong baryon number violating processes at baryon number violating processes at temperatures above 100-200 GeVtemperatures above 100-200 GeV

baryon number violation in baryon number violation in standard modelstandard model

no chemical potential for baryon numberno chemical potential for baryon number

thermal equilibrium in thermal equilibrium in absence of chemical absence of chemical

potentialpotential

baryogenesisbaryogenesis

Sakharov’s conditions forSakharov’s conditions forbaryogenesisbaryogenesis

1)1) baryon number violation baryon number violation interactionsinteractions

2)2) charge conjugation violating charge conjugation violating interactionsinteractions

3)3) CP – violating interactionsCP – violating interactions

4)4) non – equilibrium processnon – equilibrium process

baryon number violating baryon number violating processprocess

in Grand Unified Theories in Grand Unified Theories ( GUT )( GUT )

baryon number violating baryon number violating processprocess

in Grand Unified Theories in Grand Unified Theories ( GUT )( GUT )

not good enough :not good enough :

B asymmetry will be washed out later B asymmetry will be washed out later by sphaleron processesby sphaleron processes

no B-L asymmetry is producedno B-L asymmetry is produced

leptogenesis or late leptogenesis or late baryogenesisbaryogenesis

leptogenesisleptogenesis

B – L is conserved quantum B – L is conserved quantum number innumber in

standard modelstandard model sphaleron processes transmute lepton sphaleron processes transmute lepton

asymmetry into baryon asymmetryasymmetry into baryon asymmetry a fraction of primordial B-L asymmetry a fraction of primordial B-L asymmetry

appears as baryon asymmetryappears as baryon asymmetry

primordial asymmetry protected from primordial asymmetry protected from wash out by sphaleron processeswash out by sphaleron processes

( B-L )( B-L )

leptogenesisleptogenesis

non – equilibrium decay of heavy non – equilibrium decay of heavy neutrinosneutrinos

non – equilibrium production after non – equilibrium production after inflation during entropy production inflation during entropy production of the Universeof the Universe

baryogenesis during baryogenesis during electroweak phase electroweak phase

transition ?transition ?

Sakharov’s conditions forSakharov’s conditions forbaryogenesis during baryogenesis during electroweak phase electroweak phase

transitiontransition

1)1) baryon number violation interactions ☺baryon number violation interactions ☺

2)2) charge conjugation violating charge conjugation violating interactions ☺interactions ☺

3)3) CP – violating interactions ☺CP – violating interactions ☺

4)4) non – equilibrium process ☺non – equilibrium process ☺

cosmological phase cosmological phase transitionstransitions

cosmological phase cosmological phase transitionstransitions

first order cosmological first order cosmological phase transitionsphase transitions

chaos in the Universechaos in the Universe

baryogenesis during baryogenesis during electroweak phase electroweak phase

transitiontransition strongly first order electroweak strongly first order electroweak

phase transition can generate baryon phase transition can generate baryon asymmetry if CP violation is asymmetry if CP violation is sufficiently strong sufficiently strong

no efficient baryogenesis for weak no efficient baryogenesis for weak first order phase transition, second first order phase transition, second order phase transition or crossoverorder phase transition or crossover

presumably too little CP violation in presumably too little CP violation in SM ( not definitely settled )SM ( not definitely settled )

electroweak “phase electroweak “phase transition “transition “

in standard model is in standard model is crossover !crossover !

perhaps strong first order transition in perhaps strong first order transition in supersymmetric extensions of standard model supersymmetric extensions of standard model

standard model of particle standard model of particle physics and cosmologyphysics and cosmology

no candidate for dark matterno candidate for dark matter no baryon asymmetryno baryon asymmetry no massive neutrinosno massive neutrinos

standard model of particle standard model of particle physics and cosmologyphysics and cosmology

prediction :prediction :

present Universe consists ofpresent Universe consists of

photons and photons and

massless neutrinosmassless neutrinos