Download - Chiral phase transition and chemical freeze out Chiral phase transition and chemical freeze out
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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