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

2. Heavy ion collision Heavy ion collision

3. 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 (?)

4. Hadron abundancies Hadron abundancies

5. 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

6. Exclusion argument Assume T is a meaningful concept - Assume T is a meaningful concept - complex issue, to be discussed later complex issue, to be discussed later T ch < T c : hadrochemical equilibrium T ch < T c : hadrochemical equilibrium Exclude T ch much smaller than T c : Exclude T ch much smaller than T c : say T ch > 0.95 T c say T ch > 0.95 T c 0.95 < T ch /T c < 1 0.95 < T ch /T c < 1

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

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

9. 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

10. 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 !

11. 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

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

13. 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 )

14. Energy density Lattice simulations Lattice simulations Karsch et al Karsch et al even more dramatic for first order for first order transition transition

15. Phase space increases very rapidly with energy and therefore with temperature increases very rapidly with energy and therefore with temperature effective dependence of time needed to produce Ω effective dependence of time 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

16. 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

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

18. 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

19. Relevant time scale in hadronic phase rates needed for equilibration of Ω and kaons: ΔT = 5 MeV, F ΩK = 1.13, τ T =8 fm (0.02-0.2)/fm two –particle – scattering :

20. T ch ≈ T c T ch ≈ T c

21. Phase diagram Phase diagram hadrons hadrons quarks and gluons

22. Is temperature defined ? Does comparison with equilibrium critical temperature make sense ?

23. Prethermalization J.Berges,Sz.Borsanyi,CW

24. Vastly different time scales for “thermalization” of different quantities here : scalar with mass m coupled to fermions ( linear quark-meson-model ) ( linear quark-meson-model ) method : two particle irreducible non- equilibrium effective action ( J.Berges et al )

25. Thermal equilibration : occupation numbers Thermal equilibration : occupation numbers

26. Prethermalization equation of state p/ε Prethermalization equation of state p/ε similar for kinetic temperature

27. different “temperatures” different “temperatures”

28. Mode temperature n p :occupation number for momentum p late time: Bose-Einstein or Fermi-Dirac distribution

30. Kinetic equilibration before chemical equilibration Kinetic equilibration before chemical equilibration

31. Once a temperature becomes stationary it takes the value of the equilibrium temperature. Once chemical equilibration has been reached the chemical temperature equals the kinetic temperature and can be associated with the overall equilibrium temperature. Comparison of chemical freeze out temperature with critical temperature of phase transition makes sense

32. A possible source of error : temperature-dependent particle masses Chiral order parameter σ depends on T chemical freeze out measures T/m !

33. uncertainty in m(T) uncertainty in critical temperature

34. Phase diagram Phase diagram R.Pisarski = σ ≠ 0 = σ ≠ 0 =0 =0

35. Chiral symmetry restoration at high temperature High T SYM =0 =0 Low T SSB =φ 0 ≠ 0 =φ 0 ≠ 0 at high T : less order more symmetry examples: magnets, crystals

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

37. Order of the phase transition

38. Second order phase transition

39. second order phase transition for T only somewhat below T c : the order parameter σ is expected to deviate substantially from its vacuum value the order parameter σ is expected to deviate substantially from its vacuum value This seems to be disfavored by observation of chemical freeze out !

40. Ratios of particle masses and chemical freeze out Ratios of particle masses and chemical freeze out at chemical freeze out : ratios of hadron masses seem to be close to vacuum values ratios of hadron masses seem to be close to vacuum values nucleon and meson masses have different characteristic dependence on σ nucleon and meson masses have different characteristic dependence on σ m nucleon ~ σ, m π ~ σ -1/2 m nucleon ~ σ, m π ~ σ -1/2 Δσ/σ < 0.1 ( conservative ) Δσ/σ < 0.1 ( conservative )

41. systematic uncertainty : Δσ/σ=ΔT c /T c Δσ is negative

42. First order phase transition First order phase transition

43. first order phase transition seems to be favored by chemical freeze out first order phase transition seems to be favored by chemical freeze out

44. Lattice results e.g. Karsch,Laermann,Peikert Critical temperature in chiral limit : N f = 3 : T c = ( 154 ± 8 ) MeV N f = 2 : T c = ( 173 ± 8 ) MeV Chiral symmetry restoration and deconfinement at same T c

45. pressure pressure

46. realistic QCD precise lattice results not yet available precise lattice results not yet available for first order transition vs. crossover for first order transition vs. crossover also uncertainties in determination of critical temperature ( chiral limit …) also uncertainties in determination of critical temperature ( chiral limit …) extension to nonvanishing baryon number only for QCD with relatively heavy quarks extension to nonvanishing baryon number only for QCD with relatively heavy quarks

47. conclusion 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

48. end