Chiral phase Chiral phase transition andtransition and

chemical freeze chemical freeze outout

Understanding the phase Understanding the phase diagramdiagram

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 global Different realizations of global 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

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

speculation : endpoint speculation : endpoint of critical line ?of critical line ?

How to find out ?How to find out ?

MethodsMethods Lattice : Lattice : One has to wait until chiral limit One has to wait until chiral limit is properly implemented ! Non-zero is properly implemented ! Non-zero chemical potential poses problems.chemical potential poses problems. Functional renormalization :Functional renormalization : Not yet available for QCD with quarks Not yet available for QCD with quarks

and and non-zero chemical potential. Nucleons ?non-zero chemical potential. Nucleons ?

Models : Models : Simple quark meson models cannot work.Simple quark meson models cannot work.. Polyakov loops ? For low T : nucleons . Polyakov loops ? For low T : nucleons

needed.needed. Higgs picture of QCD ?Higgs picture of QCD ?

Experiment : Experiment : Has THas Tcc been measured ? been measured ?

Chemical freeze-out andChemical freeze-out and phase diagram phase diagram

hadronshadrons

Hadron abundanciesHadron abundancies

Chemical freeze-out andChemical freeze-out and phase diagram phase diagram

Chemical freeze-outChemical freeze-out

phasephasetransitiontransition//strongstrongcrossovercrossover

No phaseNo phasetransition transition or or strong strong crossovercrossover

Lessons from theLessons from thehadron worldhadron world

Chemical freeze-out at Chemical freeze-out at high baryon densityhigh baryon density

S.Floerchinger,…S.Floerchinger,…

No phase transitionNo phase transitionor crossover !or crossover !

Chiral order parameterChiral order parameter

Number densityNumber density

Linear nucleon – meson Linear nucleon – meson modelmodel

Protons, neutronsProtons, neutrons Pions , sigma-mesonPions , sigma-meson Omega-meson ( effective chemical Omega-meson ( effective chemical

potential, repulsive interaction)potential, repulsive interaction) Chiral symmetry fully realizedChiral symmetry fully realized Simple description of order parameter Simple description of order parameter

and chiral phase transitionand chiral phase transition Chiral perturbation theory recovered by Chiral perturbation theory recovered by

integrating out sigma-mesonintegrating out sigma-meson

Linear nucleon – meson Linear nucleon – meson modelmodel

Effective potential andEffective potential andthermal fluctuations thermal fluctuations

For high baryon density and low For high baryon density and low T :T :dominated by nucleon dominated by nucleon fluctuations !fluctuations !

Pressure of gas of Pressure of gas of nucleons withnucleons with

field-dependent massfield-dependent mass

Valid estimate for Valid estimate for ΔΔin indicated regionin indicated region

Input : T=0 potentialInput : T=0 potentialincludes complicated includes complicated physics of quantum physics of quantum fluctuations in QCDfluctuations in QCD

parametersparameters

determined by phenomenology of determined by phenomenology of nuclear matter. Droplet model reproduced.nuclear matter. Droplet model reproduced.Density of nuclear matter, binding energy,Density of nuclear matter, binding energy,surface tension, compressibility, order surface tension, compressibility, order parameter in nuclear matter.parameter in nuclear matter.

other parameterizations : similar resultsother parameterizations : similar results

Effective potential (T=0)Effective potential (T=0)

Effective potential for Effective potential for different Tdifferent T

Chiral order parameterChiral order parameter

FirstFirstorderordertransitiotransitionn

Endpoint of critical lineEndpoint of critical lineof first order transitionof first order transition

T = 20.7 MeVT = 20.7 MeVμ = 900 MeVμ = 900 MeV

Baryon densityBaryon density

Particle number densityParticle number density

Energy densityEnergy density

Conclusion (1)Conclusion (1) Thermodynamics Thermodynamics reliablyreliably understood understood

in indicated region of phase diagramin indicated region of phase diagram

No sign of phase transition or No sign of phase transition or crossovercrossover at experimental chemical at experimental chemical freeze-out pointsfreeze-out points

Freeze-out at line of constant number Freeze-out at line of constant number densitydensity

Has the Has the critical temperature critical temperature

of the QCD phase of 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 with Observation : statistical distribution of hadron species with “chemical freeze out temperature “ T“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 temperature is a meaningful Assume temperature is a meaningful concept -concept -

complex issuecomplex issue

TTchch < T < Tc c : : hadrohadrochemicalchemical equilibriumequilibrium

Exclude hadrochemical equilibrium at Exclude hadrochemical equilibrium at temperaturetemperature much smaller than Tmuch smaller than Tc c ::

say for temperatures < 0.95 Tsay for temperatures < 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 on T bound on Tch ch / / TTcc

Key argument Key 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 Mechanisms for production of multistrange hadronsof multistrange 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 - - productionproduction

Should 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 Very rapid density increaseincrease

……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 density Energy density

Lattice simulationsLattice simulations

Karsch et alKarsch et al

( even more ( even more dramaticdramatic

for first orderfor first order

transition )transition )

Phase spacePhase space

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

effective temperature dependence of time effective temperature dependence of time which is needed to produce which is needed to 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 !

chemical equilibrium inchemical equilibrium inhadronic phasehadronic phase

requires multi-particle scattering to requires multi-particle scattering to be importantbe important

realized for observed freeze out realized for observed freeze out temperaturetemperature

chiral phase transition chiral phase transition fromfrom

hadronic perspectivehadronic perspective

must exist for crossover ( or second must exist for crossover ( or second order phase transition )order phase transition )

critical temperature : the temperature critical temperature : the temperature when multi-particle scattering when multi-particle scattering becomes dominantbecomes dominant

coincides with freeze-out temperaturecoincides with freeze-out temperature

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

TTch ch ≈ T ≈ Tcc

Conclusion (2)Conclusion (2)

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

Conclusion (3)Conclusion (3)

temperature and chemical potential of temperature and chemical potential of phase transition should be determined phase transition should be determined from distribution of particles which from distribution of particles which change their abundance only through change their abundance only through multi-particle interactionsmulti-particle interactions

pions may still have time to change pions may still have time to change numbers numbers through few body scattering through few body scattering – results in lower freeze-out – results in lower freeze-out temperature for pionstemperature for pions

Chemical freeze-outChemical freeze-out

phasephasetransition transition //rapidrapidcrossovercrossover

No No phasephasetransitiotransitionn

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