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

Yes !Yes !

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

• not : not : “ I have a model where T“ I have a model where Tcc≈ T≈ Tch ch ““

• not :not : “ I use T “ I use Tcc as a free parameter and as a free parameter and find that in a model simulation it is find that in a model simulation it is

close to the lattice value ( or Tclose to the lattice value ( or Tchch ) “ ) “

TTch ch ≈ 176 MeV≈ 176 MeV (?) (?)

Hadron abundanciesHadron abundancies

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

TTchch≈T≈Tcc

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

Estimate of critical Estimate of critical temperaturetemperature

For TFor Tch ch ≈ 176 MeV :≈ 176 MeV :

0.95 < T0.95 < Tchch /T /Tcc

• 176 MeV < T176 MeV < Tc c < 185 MeV< 185 MeV

0.75 < T0.75 < Tchch /T /Tcc

• 176 MeV < T176 MeV < Tc c < 235 MeV< 235 MeV

Quantitative issue matters!Quantitative issue matters!

needed :needed :

lowerlower bound bound onon TTchch/ T/ Tcc

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 “ : dominant only in production “ : dominant only in immediateimmediate vicinity of T vicinity of Tcc

Mechanisms for production of Mechanisms for production of multistrange hadronsmultistrange hadrons

Many 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 models

Necessary 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

Rates for multiparticle Rates for multiparticle scatteringscattering

2 pions + 3 kaons -> 2 pions + 3 kaons -> ΩΩ + antiproton + antiproton

Very rapid density increaseVery rapid density increase

……in vicinity of critical temperaturein vicinity of critical temperature

Extremely rapid increase of rate of Extremely rapid increase of rate of multiparticle scattering processesmultiparticle scattering processes

( proportional to very high power of ( proportional to very high power of density )density )

Energy densityEnergy density

Lattice simulationsLattice simulations

Karsch et alKarsch et al

even more even more dramaticdramatic

for first orderfor first order

transitiontransition

Phase spacePhase space

• increases very rapidly with energy and increases very rapidly with energy and therefore with temperaturetherefore with temperature

• effective dependence of time needed to effective dependence of time needed to produce produce ΩΩ

ττΩΩ ~ T ~ T -60-60 ! !

This will even be more dramatic if transition is This will even be more dramatic if transition is closer to first order phase transitioncloser to first order phase transition

Production time for Production time for ΩΩ

multi-meson multi-meson scatteringscattering

ππ++ππ++ππ+K+K ->+K+K -> ΩΩ+p+p

strong strong dependence on dependence on pion densitypion density

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

enough time for enough time for ΩΩ - - productionproduction

at T=176 MeV :at T=176 MeV :

ττΩΩ ~ 2.3 fm~ 2.3 fm

consistency !consistency !

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

Relevant time scale in hadronic Relevant time scale in hadronic phasephase

rates needed for equilibration of rates needed for equilibration of ΩΩ and kaons: and kaons:

ΔΔT = 5 MeV, T = 5 MeV, FFΩΩK K = 1.13 ,= 1.13 ,ττT T =8 fm=8 fm

(0.02-0.2)/fm(0.02-0.2)/fm

two –particle – scattering :two –particle – scattering :

TTch ch ≈ T ≈ Tcc

Phase diagramPhase diagram

hadrons hadrons

quarks and gluonsquarks and gluons

Is temperature defined ?Is temperature defined ?

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

PrethermalizationPrethermalization

J.Berges,Sz.Borsanyi,CWJ.Berges,Sz.Borsanyi,CW

Vastly different time scalesVastly different time scales

for “thermalization” of different for “thermalization” of different quantitiesquantities

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 ) )

Thermal equilibration :Thermal equilibration : occupation numbers occupation numbers

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

A possible source of error : A possible source of error : temperature-dependent particle temperature-dependent particle massesmasses

Chiral order parameter Chiral order parameter σσ depends on T depends on T

chemical chemical freeze freeze outoutmeasuremeasuressT/m !T/m !

uncertainty in m(T)uncertainty in m(T)

uncertainty in critical uncertainty in critical temperaturetemperature

Phase diagramPhase diagram

R.PisarskiR.Pisarski

<<φφ>= >= σσ ≠≠ 0 0

<<φφ>=>=00

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

High THigh TSYM SYM <<φφ>=0>=0

Low TLow T

SSBSSB

<<φφ>=>=φφ0 0

≠≠ 0 0at high T :at high T :

less orderless order

more symmetrymore symmetry

examples:examples:

magnets, crystalsmagnets, crystals

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

Order ofOrder ofthethephasephasetransitiontransition

Second order phase Second order phase transitiontransition

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 expected to is expected to deviate substantially from its vacuum deviate substantially from its vacuum valuevalue

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

RatiosRatios of particle masses and of particle masses and chemical freeze out chemical freeze out

at 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 )

systematic uncertainty :systematic uncertainty :

ΔσΔσ//σσ==ΔΔTTcc/T/Tcc

ΔσΔσ is negativeis negative

First order phase First order phase transitiontransition

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

Lattice resultsLattice results

e.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

conclusionconclusion

• experimental determination of experimental determination of critical temperature may be critical temperature may be more precise than lattice resultsmore precise than lattice results

• error estimate becomes crucialerror estimate becomes crucial

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