Phase transitions Phase transitions in the early universe in the early universe

Cosmological phase Cosmological phase transition…transition………when the universe cools below 175 when the universe cools below 175

MeVMeV

1010-5 -5 seconds after the big bangseconds after the big bang

Quarks and gluons form baryons and Quarks and gluons form baryons and mesonsmesons

before: simply not enough volume per particle before: simply not enough volume per particle availableavailable

Heavy ion Heavy ion collisioncollision

Phase Phase transition ?transition ?

Seen in Seen in experiment ?experiment ?

Cosmological relics ?Cosmological relics ?• Only if transition is first orderOnly if transition is first order• Out of equilibrium physics is crucialOut of equilibrium physics is crucial• Otherwise : the universe forgets detailed Otherwise : the universe forgets detailed

initial conditions after phase transitioninitial conditions after phase transition• In thermal equilibrium only a few In thermal equilibrium only a few

quantities like temperature T or quantities like temperature T or chemical potential chemical potential μμ determine the state determine the state

Cosmological phase Cosmological phase transitionstransitions• QCD phase transition T=175 MeVQCD phase transition T=175 MeV• Electroweak phase transition T=150 GeVElectroweak phase transition T=150 GeV baryogenesisbaryogenesis ??• GUT phase transition(s) ? T=10GUT phase transition(s) ? T=101616 GeV GeV monopoles,cosmic strings ?monopoles,cosmic strings ?• ““inflation” T=10inflation” T=101515 GeV GeV primordial density fluctuations !primordial density fluctuations ! primordial magnetic fields ?primordial magnetic fields ?

Order of the phase transition is Order of the phase transition is crucial ingredient for crucial ingredient for cosmological phase transition cosmological phase transition and experiments and experiments ( heavy ion collisions )( heavy ion collisions )

Order ofOrder ofthethephasephasetransitiontransition

temperature temperature dependence ofdependence oforder parameterorder parameter

Second order phase Second order phase transitiontransition

First order phase First order phase transitiontransition

Electroweak phase Electroweak phase transition ?transition ?

• 1010-12 -12 s after big bangs after big bang• fermions and W-,Z-bosons get massfermions and W-,Z-bosons get mass• standard model : crossoverstandard model : crossover• baryogenesis if first orderbaryogenesis if first order ( only for some SUSY – models )( only for some SUSY – models ) bubble formation of “ our vacuum “bubble formation of “ our vacuum “

Reuter,Wetterich ‘93Reuter,Wetterich ‘93

Kuzmin,Rubakov,Shaposhnikov ‘85 , Shaposhnikov ‘87Kuzmin,Rubakov,Shaposhnikov ‘85 , Shaposhnikov ‘87

Electroweak phase diagramElectroweak phase diagram

M.Reuter,C.WetterichM.Reuter,C.WetterichNucl.Phys.B408,91(1993)Nucl.Phys.B408,91(1993)

Masses of excitations (d=3)Masses of excitations (d=3)

O.Philipsen,M.Teper,H.Wittig ‘97

small MH large MH

ContinuityContinuity

Higgs phase and Higgs phase and confinementconfinementcan be equivalent –can be equivalent – then simply two different descriptions then simply two different descriptions

(pictures) of the same physical situation(pictures) of the same physical situationIs this realized for QCD ?Is this realized for QCD ?Necessary condition : spectrum of Necessary condition : spectrum of

excitations with the same quantum excitations with the same quantum numbers in both picturesnumbers in both pictures

- known for QCD : mesons + baryons -- known for QCD : mesons + baryons -

QCD at high temperatureQCD at high temperature

• Quark – gluon plasmaQuark – gluon plasma• Chiral symmetry restoredChiral symmetry restored• ““Deconfinement” ( no linear heavy Deconfinement” ( no linear heavy

quark potential at large distances )quark potential at large distances )• Lattice simulations : both effects Lattice simulations : both effects

happen at the same temperaturehappen at the same temperature

Chiral symmetry restoration Chiral symmetry restoration at high temperature at high temperature

High THigh TSYM SYM <<φφ>=0>=0

Low TLow TSSBSSB<<φφ>=>=φφ

0 0 ≠≠ 0 0

at high T :at high T :less orderless ordermore symmetrymore symmetry

examples:examples:magnets, crystalsmagnets, crystals

QCD – phase transitionQCD – phase transition Quark –gluon plasmaQuark –gluon plasma

• Gluons : 8 x 2 = 16Gluons : 8 x 2 = 16• Quarks : 9 x 7/2 =12.5Quarks : 9 x 7/2 =12.5• Dof : 28.5Dof : 28.5

Chiral symmetryChiral symmetry

Hadron gasHadron gas

• Light mesons : 8Light mesons : 8• (pions : 3 )(pions : 3 )• Dof : 8Dof : 8

Chiral sym. brokenChiral sym. brokenLarge difference in number of degrees of freedom !Large difference in number of degrees of freedom !Strong increase of density and energy density at TStrong increase of density and energy density at Tcc !!

Understanding the phase Understanding the phase diagramdiagram

quark-gluon quark-gluon plasmaplasma““deconfinement”deconfinement”

quark matter : quark matter : superfluidsuperfluidB spontaneously B spontaneously brokenbroken

nuclear matter : B,isospin (I3) spontaneously nuclear matter : B,isospin (I3) spontaneously broken, broken, S conservedS conserved

Phase diagram for ms > mu,dPhase diagram for ms > mu,d

vacuumvacuum

Order parametersOrder parameters

• Nuclear matter and quark matter are Nuclear matter and quark matter are separated from other phases by true separated from other phases by true critical linescritical lines

• Different realizations of Different realizations of globalglobal symmetriessymmetries

• Quark matter: SSB of baryon number BQuark matter: SSB of baryon number B• Nuclear matter: SSB of combination of B Nuclear matter: SSB of combination of B

and isospin Iand isospin I3 3 neutron-neutron condensateneutron-neutron condensate

quark-gluon plasmaquark-gluon plasma““deconfinement”deconfinement”

quark matter : superfluidquark matter : superfluidB spontaneously brokenB spontaneously broken

nuclear matter :nuclear matter :B,isospin (I3) spontaneously broken, S conservedB,isospin (I3) spontaneously broken, S conserved

vacuumvacuum

Phase diagram for ms > mu,dPhase diagram for ms > mu,d

““minimal” phase diagramminimal” phase diagram for equal nonzero quark massesfor equal nonzero quark masses

Endpoint of critical line ?Endpoint of critical line ?

How to find out ?How to find out ?

MethodsMethods• Lattice :Lattice : You have to wait until chiral limit You have to wait until chiral limit is properly implemented !is properly implemented !

• Models :Models : Quark meson models cannot Quark meson models cannot workwork

Higgs picture of QCD ?Higgs picture of QCD ?

• Experiment :Experiment : Has THas Tcc been measured ? been measured ? Indications for Indications for first order transition !first order transition !

LatticeLattice

Lattice resultsLattice resultse.g. Karsch,Laermann,Peikerte.g. Karsch,Laermann,Peikert

Critical temperature in chiral limit :Critical temperature in chiral limit :

NNff = 3 : T = 3 : Tcc = ( 154 ± 8 ) MeV = ( 154 ± 8 ) MeVNNff = 2 : T = 2 : Tcc = ( 173 ± 8 ) MeV = ( 173 ± 8 ) MeV

Chiral symmetry restoration and Chiral symmetry restoration and deconfinement at same Tdeconfinement at same Tcc

pressurepressure

realistic QCDrealistic QCD

• precise lattice results not yet availableprecise lattice results not yet available for first order transition vs. crossoverfor first order transition vs. crossover• also uncertainties in determination of also uncertainties in determination of

critical temperature ( chiral limit …)critical temperature ( chiral limit …)• extension to nonvanishing baryon extension to nonvanishing baryon

number only for QCD with relatively number only for QCD with relatively heavy quarksheavy quarks

ModelsModels

Analytical description of Analytical description of phase transition phase transition

• Needs model that can account Needs model that can account simultaneously for the correct simultaneously for the correct degrees of freedom below and above degrees of freedom below and above the transition temperature.the transition temperature.

• Partial aspects can be described by Partial aspects can be described by more limited models, e.g. chiral more limited models, e.g. chiral properties at small momenta. properties at small momenta.

Universe cools below 175 MeV…Universe cools below 175 MeV…

Both gluons and quarks disappear fromBoth gluons and quarks disappear from thermal equilibrium : mass generationthermal equilibrium : mass generation Chiral symmetry breaking Chiral symmetry breaking mass for fermionsmass for fermions Gluons ?Gluons ?

Analogous situation in electroweak phase Analogous situation in electroweak phase transition understood by Higgs mechanismtransition understood by Higgs mechanism

Higgs description of QCD vacuum ?Higgs description of QCD vacuum ?

Higgs phase and Higgs phase and confinementconfinementcan be equivalent –can be equivalent – then simply two different descriptions then simply two different descriptions

(pictures) of the same physical situation(pictures) of the same physical situationIs this realized for QCD ?Is this realized for QCD ?Necessary condition : spectrum of Necessary condition : spectrum of

excitations with the same quantum excitations with the same quantum numbers in both picturesnumbers in both pictures

Higgs picture with mesons,baryons as Higgs picture with mesons,baryons as excitations?excitations?

Higgs picture of QCDHiggs picture of QCD ““spontaneous breaking of color “spontaneous breaking of color “ in the QCD – vacuumin the QCD – vacuum

octet condensateoctet condensate

for Nfor Nf f = 3 ( u,d,s )= 3 ( u,d,s )

C.Wetterich, Phys.Rev.D64,036003(2001),hep-ph/0008150

Quark –antiquark Quark –antiquark condensatecondensate

Octet condensateOctet condensate < octet > ≠ 0 :< octet > ≠ 0 :•““Spontaneous breaking of color”Spontaneous breaking of color”•Higgs mechanismHiggs mechanism•Massive Gluons – all masses equalMassive Gluons – all masses equal•Eight octets have vevEight octets have vev• Infrared regulator for QCDInfrared regulator for QCD

Flavor symmetryFlavor symmetry for equal quark masses :for equal quark masses :

octet preserves global SU(3)-symmetryoctet preserves global SU(3)-symmetry “ “diagonal in color and flavor”diagonal in color and flavor” “ “color-flavor-locking”color-flavor-locking” (cf. Alford,Rajagopal,Wilczek ; Schaefer,Wilczek)(cf. Alford,Rajagopal,Wilczek ; Schaefer,Wilczek)

All particles fall into representations ofAll particles fall into representations of the “eightfold way”the “eightfold way”

quarks : 8 + 1 , gluons : 8quarks : 8 + 1 , gluons : 8

Quarks and gluons carry the Quarks and gluons carry the observed quantum numbers of observed quantum numbers of isospin and strangenessisospin and strangenessof the baryon and of the baryon and vector meson octets !vector meson octets !

They are integer charged!They are integer charged!

Low energy effective actionLow energy effective action

γ=φ+χ

……accounts for accounts for massesmasses and and couplingscouplings of light of light pseudoscalars, vector-pseudoscalars, vector-mesons and baryons !mesons and baryons !

Phenomenological Phenomenological parametersparameters• 5 undetermined 5 undetermined

parametersparameters• predictionspredictions

Chiral perturbation theoryChiral perturbation theory+ all predictions of chiral perturbation + all predictions of chiral perturbation

theorytheory+ determination of parameters+ determination of parameters

Chiral phase transition Chiral phase transition at high temperatureat high temperatureHigh temperature phase transition in QCD :High temperature phase transition in QCD : Melting of octet condensateMelting of octet condensate

Lattice simulations :Lattice simulations :Deconfinement temperature = critical Deconfinement temperature = critical

temperature for restoration of chiral temperature for restoration of chiral symmetrysymmetry

Why ?Why ?

Simple explanation :Simple explanation :

Higgs picture of the QCD-phase Higgs picture of the QCD-phase transitiontransition

A simple mean field calculation A simple mean field calculation gives roughly reasonable description gives roughly reasonable description that should be improved.that should be improved.

TTcc =170 MeV =170 MeV First order transitionFirst order transition

ExperimentExperiment

Has the Has the critical temperature of critical temperature of the QCD phase the QCD phase transition been transition been measured ?measured ?

Heavy ion collisionHeavy ion collision

Chemical freeze-out Chemical freeze-out temperaturetemperature T Tch ch =176 MeV=176 MeV

hadron abundancieshadron abundancies

Exclusion argumentExclusion argumenthadronic phasehadronic phasewith sufficient with sufficient production of production of ΩΩ : : excluded !!excluded !!

Exclusion argumentExclusion argument Assume T is a meaningful concept -Assume T is a meaningful concept - complex issue, to be discussed latercomplex issue, to be discussed later

TTchch < T < Tc c : : hadrohadrochemical equilibriumchemical equilibrium

Exclude TExclude Tch ch much smaller than Tmuch smaller than Tcc :: say Tsay Tchch > 0.95 T > 0.95 Tcc

0.95 < T0.95 < Tchch /T /Tcc < 1 < 1

Has THas Tc c been measured ?been measured ?• Observation : statistical distribution of hadron species Observation : statistical distribution of hadron species

with “chemical freeze out temperature “ Twith “chemical freeze out temperature “ Tchch=176 MeV=176 MeV

• TTch ch cannot be much smaller than Tcannot be much smaller than Tc c : hadronic rates for : hadronic rates for T< TT< Tc c are too small to produce multistrange hadrons (are too small to produce multistrange hadrons (ΩΩ,..),..)

• Only near TOnly near Tc c multiparticle scattering becomes important multiparticle scattering becomes important ( collective excitations …) – proportional to high power of ( collective excitations …) – proportional to high power of

densitydensity

P.Braun-Munzinger,J.Stachel,C.Wetterich, Phys.Lett.B P.Braun-Munzinger,J.Stachel,C.Wetterich, Phys.Lett.B (2004)(2004)

TTchch≈T≈Tcc

TTch ch ≈ T ≈ Tcc

Phase diagramPhase diagram

<<φφ>= >= σσ ≠≠ 0 0

<<φφ>≈>≈00

Temperature Temperature dependence of dependence of chiral order parameter chiral order parameter

Does experiment indicate Does experiment indicate a first order phase a first order phase transition for transition for μμ = 0 ? = 0 ?

Second order phase Second order phase transitiontransition

for T only somewhat below Tfor T only somewhat below Tc c :: the order parameter the order parameter σσ is is

expected toexpected to be close to zero andbe close to zero and deviate substantially from its deviate substantially from its

vacuum valuevacuum value

This seems to be disfavored by This seems to be disfavored by observation of chemical observation of chemical freeze out !freeze out !

Temperature dependent Temperature dependent massesmasses

• Chiral order parameter Chiral order parameter σσ depends depends on Ton T

• Particle masses depend on Particle masses depend on σσ • Chemical freeze out measures m/T Chemical freeze out measures m/T

for many speciesfor many species• Mass ratios at T just below TMass ratios at T just below Tcc are are close to vacuum ratiosclose to vacuum ratios

RatiosRatios of particle masses and of particle masses and chemical freeze out chemical freeze outat chemical freeze out :at chemical freeze out :

• ratios of hadron masses seem to be close to ratios of hadron masses seem to be close to vacuum valuesvacuum values

• nucleon and meson masses have different nucleon and meson masses have different characteristic dependence on characteristic dependence on σσ

• mmnucleon nucleon ~ ~ σσ , m , mππ ~ ~ σσ -1/2-1/2

• ΔσΔσ/σ < 0.1 ( conservative ) /σ < 0.1 ( conservative )

first order phase first order phase transitiontransition seems to be favored by seems to be favored by chemical freeze out chemical freeze out

……or extremely rapid crossoveror extremely rapid crossover

conclusionconclusion

• Experimental determination of critical Experimental determination of critical temperature may be more precise than temperature may be more precise than lattice resultslattice results

• Rather simple phase structure is suggestedRather simple phase structure is suggested• Analytical understanding is only at beginningAnalytical understanding is only at beginning

endend

How How farfar has first order line been has first order line been measured?measured?

hadrons hadrons

quarks and gluonsquarks and gluons

hadronic phasehadronic phasewith sufficient with sufficient production of production of ΩΩ :: excluded !!excluded !!

Exclusion argument for large Exclusion argument for large densitydensity

First order phase transition lineFirst order phase transition line

hadrons hadrons

quarks and gluonsquarks and gluons

μμ=923MeV=923MeVtransition totransition to nuclearnuclear matter matter

quark-gluon plasmaquark-gluon plasma““deconfinement”deconfinement”

quark matter : superfluidquark matter : superfluidB spontaneously brokenB spontaneously broken

nuclear matter :nuclear matter :B,isospin (I3) spontaneously broken, S conservedB,isospin (I3) spontaneously broken, S conserved

vacuumvacuum

Phase diagram for ms > mu,dPhase diagram for ms > mu,d

Is temperature defined ?Is temperature defined ?

Does comparison with Does comparison with equilibrium critical equilibrium critical temperature make sense ?temperature make sense ?

PrethermalizationPrethermalizationJ.Berges,Sz.Borsanyi,CWJ.Berges,Sz.Borsanyi,CW

Scalar – fermion – model with Yukawa couplingScalar – fermion – model with Yukawa coupling

bulk quantitybulk quantity mode quantitymode quantity

Vastly different time scalesVastly different time scales

for “thermalization” of different quantitiesfor “thermalization” of different quantities

here : scalar with mass m coupled to fermions here : scalar with mass m coupled to fermions ( linear quark-meson-model )( linear quark-meson-model )method : two particle irreducible non- method : two particle irreducible non-

equilibrium effective action ( equilibrium effective action ( J.Berges et alJ.Berges et al ) )

PrethermalizationPrethermalization equation of state p/ equation of state p/εε

similar for kinetic temperaturesimilar for kinetic temperature

different “temperatures”different “temperatures”

Mode temperatureMode temperature

nnpp :occupation number :occupation number for momentum pfor momentum p

late time:late time:Bose-Einstein orBose-Einstein orFermi-Dirac distributionFermi-Dirac distribution

Kinetic equilibration beforeKinetic equilibration before chemical equilibration chemical equilibration

Once a temperature becomes Once a temperature becomes stationary it takes the value of the stationary it takes the value of the equilibrium temperature.equilibrium temperature.

Once chemical equilibration has been Once chemical equilibration has been reached the chemical temperature reached the chemical temperature equals the kinetic temperature and equals the kinetic temperature and can be associated with the overall can be associated with the overall equilibrium temperature.equilibrium temperature.

Comparison of chemical freeze out Comparison of chemical freeze out temperature with critical temperaturetemperature with critical temperature of phase transition makes senseof phase transition makes sense

Key argumentKey argument

• Two particle scattering rates not Two particle scattering rates not sufficient to produce sufficient to produce ΩΩ

• ““multiparticle scattering for multiparticle scattering for ΩΩ-production -production “ : dominant only in “ : dominant only in immediateimmediate vicinity vicinity of Tof Tcc

Mechanisms for production of Mechanisms for production of multistrange hadronsmultistrange hadronsMany proposalsMany proposals

• HadronizationHadronization• Quark-hadron equilibriumQuark-hadron equilibrium• Decay of collective excitation (Decay of collective excitation (σσ – –

field )field )• Multi-hadron-scatteringMulti-hadron-scattering

Different pictures !Different pictures !

Hadronic picture of Hadronic picture of ΩΩ - - productionproductionShould exist, at least semi-quantitatively, if Should exist, at least semi-quantitatively, if TTchch < T < Tcc ( for T( for Tchch = T = Tc c : T: Tchch>0.95 T>0.95 Tc c is fulfilled anyhow )is fulfilled anyhow )

e.g. collective excitations ≈ multi-hadron-scatteringe.g. collective excitations ≈ multi-hadron-scattering (not necessarily the best and simplest picture )(not necessarily the best and simplest picture )

multihadron -> multihadron -> ΩΩ + X should have sufficient rate + X should have sufficient rate

Check of consistency for many modelsCheck of consistency for many modelsNecessary if Necessary if TTchch≠ T≠ Tcc and temperature is defined and temperature is defined Way to give Way to give quantitativequantitative bound on T bound on Tch ch / T/ Tcc

Energy densityEnergy density

Lattice simulationsLattice simulations Karsch et alKarsch et al

even more even more dramaticdramatic

for first orderfor first order transitiontransition

Production time for Production time for ΩΩmulti-meson multi-meson

scatteringscattering

ππ++ππ++ππ+K+K ->+K+K -> ΩΩ+p+p

strong strong dependence on dependence on “pion” density“pion” density

P.Braun-Munzinger,J.Stachel,CWP.Braun-Munzinger,J.Stachel,CW

extremely rapid changeextremely rapid change

lowering T by 5 MeV below critical lowering T by 5 MeV below critical temperature :temperature :

rate of rate of ΩΩ – production decreases by – production decreases by factor 10factor 10

This restricts chemical freeze out to close This restricts chemical freeze out to close vicinity of critical temperaturevicinity of critical temperature

0.95 < T0.95 < Tchch /T /Tcc < 1 < 1