1. Chiral phase transition and chemical freeze out Chiral phase transition and chemical freeze out

2. Understanding the phase diagram

3. Order parameters Nuclear matter and quark matter are separated from other phases by true critical lines Nuclear matter and quark matter are separated from other phases by true critical lines Different realizations of global symmetries Different realizations of global symmetries Quark matter: SSB of baryon number B Quark matter: SSB of baryon number B Nuclear matter: SSB of combination of B and isospin I 3 Nuclear matter: SSB of combination of B and isospin I 3 neutron-neutron condensate neutron-neutron condensate

4. “minimal” phase diagram for nonzero quark masses “minimal” phase diagram for nonzero quark masses

5. speculation : endpoint of critical line ? speculation : endpoint of critical line ?

6. How to find out ? How to find out ?

7. Methods Lattice : One has to wait until chiral limit Lattice : 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 and Not yet available for QCD with quarks and non-zero chemical potential. Nucleons ? non-zero chemical potential. Nucleons ? Models : Simple quark meson models cannot work. Models : Simple quark meson models cannot work.. Polyakov loops ? For low T : nucleons needed. Higgs picture of QCD ? Higgs picture of QCD ? Experiment : Has T c been measured ? Experiment : Has T c been measured ?

8. Chemical freeze-out and phase diagram hadrons

9. Hadron abundancies Hadron abundancies

10. Chemical freeze-out and phase diagram

11. Chemical freeze-out phasetransition/strongcrossover No phase transition or strong crossover

12. Lessons from the hadron world

13. Chemical freeze-out at high baryon density S.Floerchinger,… No phase transition or crossover !

14. Chiral order parameter

15. Number density

16. Linear nucleon – meson model Protons, neutrons Protons, neutrons Pions, sigma-meson Pions, sigma-meson Omega-meson ( effective chemical potential, repulsive interaction) Omega-meson ( effective chemical potential, repulsive interaction) Chiral symmetry fully realized Chiral symmetry fully realized Simple description of order parameter and chiral phase transition Simple description of order parameter and chiral phase transition Chiral perturbation theory recovered by integrating out sigma-meson Chiral perturbation theory recovered by integrating out sigma-meson

17. Linear nucleon – meson model

18. Effective potential and thermal fluctuations For high baryon density and low T : dominated by nucleon fluctuations !

19. Pressure of gas of nucleons with field-dependent mass

20. Valid estimate for Δ in indicated region

21. Input : T=0 potential includes complicated physics of quantum fluctuations in QCD

22. parameters determined by phenomenology of nuclear matter. Droplet model reproduced. Density of nuclear matter, binding energy, surface tension, compressibility, order parameter in nuclear matter. other parameterizations : similar results

23. Effective potential (T=0)

24. Effective potential for different T

25. Chiral order parameter Firstordertransition

26. Endpoint of critical line of first order transition T = 20.7 MeV μ = 900 MeV

27. Baryon density

28. Particle number density

29. Energy density

30. Conclusion (1) Thermodynamics reliably understood in indicated region of phase diagram Thermodynamics reliably understood in indicated region of phase diagram No sign of phase transition or crossover at experimental chemical freeze-out points No sign of phase transition or crossover at experimental chemical freeze-out points Freeze-out at line of constant number density Freeze-out at line of constant number density

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

32. Heavy ion collision Heavy ion collision

33. Yes ! 0.95 T c < T ch < T c 0.95 T c < T ch < T c not : “ I have a model where T c ≈ T ch “ not : “ I have a model where T c ≈ T ch “ not : “ I use T c as a free parameter and not : “ I use T c 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 T ch ) “ close to the lattice value ( or T ch ) “ T ch ≈ 176 MeV T ch ≈ 176 MeV

34. Hadron abundancies Hadron abundancies

35. Has T c been measured ? Observation : statistical distribution of hadron species with “chemical freeze out temperature “ T ch =176 MeV Observation : statistical distribution of hadron species with “chemical freeze out temperature “ T ch =176 MeV T ch cannot be much smaller than T c : hadronic rates for T ch cannot be much smaller than T c : hadronic rates for T< T c are too small to produce multistrange hadrons (Ω,..) T< T c are too small to produce multistrange hadrons (Ω,..) Only near T c multiparticle scattering becomes important Only near T c multiparticle scattering becomes important ( collective excitations …) – proportional to high power of density ( collective excitations …) – proportional to high power of density P.Braun-Munzinger,J.Stachel,CW T ch ≈T c

36. Exclusion argument Assume temperature is a meaningful concept - Assume temperature is a meaningful concept - complex issue complex issue T ch < T c : hadrochemical equilibrium T ch < T c : hadrochemical equilibrium Exclude hadrochemical equilibrium at temperature much smaller than T c : Exclude hadrochemical equilibrium at temperature much smaller than T c : say for temperatures < 0.95 T c say for temperatures < 0.95 T c 0.95 < T ch /T c < 1 0.95 < T ch /T c < 1

37. Estimate of critical temperature For T ch ≈ 176 MeV : 0.95 < T ch /T c 0.95 < T ch /T c 176 MeV < T c < 185 MeV 176 MeV < T c < 185 MeV 0.75 < T ch /T c 0.75 < T ch /T c 176 MeV < T c < 235 MeV 176 MeV < T c < 235 MeV Quantitative issue matters!

38. needed : lower bound on T ch / T c

39. Key argument Two particle scattering rates not sufficient to produce Ω Two particle scattering rates not sufficient to produce Ω “multiparticle scattering for Ω-production “ : dominant only in immediate vicinity of T c “multiparticle scattering for Ω-production “ : dominant only in immediate vicinity of T c

40. Mechanisms for production of multistrange hadrons Many proposals Hadronization Hadronization Quark-hadron equilibrium Quark-hadron equilibrium Decay of collective excitation (σ – field ) Decay of collective excitation (σ – field ) Multi-hadron-scattering Multi-hadron-scattering Different pictures ! Different pictures !

41. Hadronic picture of Ω - production Should exist, at least semi-quantitatively, if T ch < T c ( for T ch = T c : T ch >0.95 T c is fulfilled anyhow ) ( for T ch = T c : T ch >0.95 T c is fulfilled anyhow ) e.g. collective excitations ≈ multi-hadron-scattering (not necessarily the best and simplest picture ) (not necessarily the best and simplest picture ) multihadron -> Ω + X should have sufficient rate Check of consistency for many models Necessary if T ch ≠ T c and temperature is defined Way to give quantitative bound on T ch / T c

42. Rates for multiparticle scattering 2 pions + 3 kaons -> Ω + antiproton

43. Very rapid density increase …in vicinity of critical temperature Extremely rapid increase of rate of multiparticle scattering processes ( proportional to very high power of density )

44. Energy density Lattice simulations Lattice simulations Karsch et al Karsch et al ( even more dramatic for first order for first order transition ) transition )

45. Phase space increases very rapidly with energy and therefore with temperature increases very rapidly with energy and therefore with temperature effective temperature dependence of time which is needed to produce Ω effective temperature dependence of time which is needed to produce Ω τ Ω ~ T -60 ! τ Ω ~ T -60 ! This will even be more dramatic if transition is closer to first order phase transition

46. Production time for Ω multi-meson scattering π+π+π+K+K -> Ω+p Ω+p strong dependence on pion density strong dependence on pion density P.Braun-Munzinger,J.Stachel,CW

47. enough time for Ω - production at T=176 MeV : τ Ω ~ 2.3 fm τ Ω ~ 2.3 fm consistency ! consistency !

48. chemical equilibrium in hadronic phase requires multi-particle scattering to be important requires multi-particle scattering to be important realized for observed freeze out temperature realized for observed freeze out temperature

49. chiral phase transition from hadronic perspective must exist for crossover ( or second order phase transition ) must exist for crossover ( or second order phase transition ) critical temperature : the temperature when multi-particle scattering becomes dominant critical temperature : the temperature when multi-particle scattering becomes dominant coincides with freeze-out temperature coincides with freeze-out temperature

50. extremely rapid change lowering T by 5 MeV below critical temperature : lowering T by 5 MeV below critical temperature : rate of Ω – production decreases by rate of Ω – production decreases by factor 10 factor 10 This restricts chemical freeze out to close vicinity of critical temperature This restricts chemical freeze out to close vicinity of critical temperature 0.95 < T ch /T c < 1 0.95 < T ch /T c < 1

51. T ch ≈ T c T ch ≈ T c

52. Conclusion (2) experimental determination of critical temperature may be more precise than lattice results experimental determination of critical temperature may be more precise than lattice results error estimate becomes crucial error estimate becomes crucial

53. Conclusion (3) temperature and chemical potential of phase transition should be determined from distribution of particles which change their abundance only through multi-particle interactions temperature and chemical potential of phase transition should be determined from distribution of particles which change their abundance only through multi-particle interactions pions may still have time to change numbers through few body scattering – results in lower freeze-out temperature for pions pions may still have time to change numbers through few body scattering – results in lower freeze-out temperature for pions

54. Chemical freeze-out phase transition / rapidcrossover No phase transition

55. end