1. The QCD Phase Diagram in Relativistic Heavy Ion Collisions October 24, 2011@KMI Inauguration Conference Chiho NONAKA, Nagoya University

2. C.NONAKA KMIIN Strongly Interacting QGP Hadron Phase Color Super Conductor QCD Critical Point Quark-Gluon Plasma 高 陽子、中間子など T BB sQGP Heavy Ion Collisions ： LHC,RHIC Relativistic hydrodynamics Recombination model Jet quenching Color Glass Condensate RHIC:2000 LHC: Energy frontier RHIC, SPS: energy scan FAIR, NICA ： high density Property of QGP

3. C.NONAKA KMIIN QCD Experiments AGS, SPS, RHIC, LHC lattice QCD effective theory ? Our Approach Phenomenological analyses relativistic hydrodynamic model event generator statistical model… Realistic dynamical model QGP signal? RHIC, LHC…

4. C.NONAKA KMIIN Strongly Interacting QGP Hadron Phase Color Super Conductor QCD Critical Point Quark-Gluon Plasma 高 陽子、中間子など T BB Phenomenological analyses Relativistic hydrodynamics Recombination model Lattice QCD: hadron property Phenomenological analyses Relativistic hydrodynamics Recombination model Lattice QCD: hadron property sQGP Heavy Ion Collisions ： LHC,RHIC

5. C.NONAKA KMIIN Multi Module Modeling Relativistic Heavy Ion Collisions 3D Ideal hydro + UrQMD model thermalization hydrohadronizationfreezeout Full 3-d Hydrodynamics EoS :1st order phase transition QGP + excluded volume model Cooper-Frye formula UrQMD t fm/c final state interactions Monte Carlo Hadronization TCTC T SW T C :critical temperature T SW : Hydro  UrQMD collisions

6. C.NONAKA KMIIN Nonaka and Bass PRC75:014902(2007) Highlights of 3D hydro+UrQMD @RHIC

7. C.NONAKA KMIIN Strongly Interacting QGP Hadron Phase Color Super Conductor QCD Critical Point Quark-Gluon Plasma 高 陽子、中間子など T BB Phenomenological analyses Relativistic hydrodynamics Recombination model Lattice QCD: hadron property Phenomenological analyses Relativistic hydrodynamics Recombination model Lattice QCD: hadron property sQGP Heavy Ion Collisions ： LHC,RHIC

8. C.NONAKA KMIIN Quark Number Scaling Elliptic flow – Quarks – Hadrons (meson) Quark number scaling mesonbaryon R.J. Fries, C. Nonaka, B. Mueller & S.A. Bass, PRL 90 202303 (2003) R.J. Fries, C. Nonaka, B. Mueller & S.A. Bass, PRC 68 044902 (2003) C. Nonaka, R.J. Fries & S.A. Bass, Phys. Lett. B583 73-78 (2004) C. Nonaka, B. Mueller, M. Asakawa, S.A. Bass & R.J. Fries, PRC 69 031902 (2004)

9. C.NONAKA KMIIN Elliptic Flow Mesons Baryons Meson Baryon Nuclear modification factor Hadron ratios Quark number scaling:

10. C.NONAKA KMIIN Multi Module Modeling Our plan thermalization hydrohadronizationfreezeout collisions hydrodynamic model + viscosity Initial fluctuationfinal state interactions Targets: higher harmonics, jets in medium and so on @QM2011

11. C.NONAKA KMIIN Strongly Interacting QGP Hadron Phase Color Super Conductor QCD Critical Point Quark-Gluon Plasma 高 陽子、中間子など T BB Phenomenological analyses Relativistic hydrodynamics Recombination model Lattice QCD: hadron property Phenomenological analyses Relativistic hydrodynamics Recombination model Lattice QCD: hadron property sQGP Heavy Ion Collisions ： LHC,RHIC

12. C.NONAKA KMIIN J/  Suppression QGP signature in heavy ion collisions Current situation – Experiments: SPS, RHIC, LHC – Lattice QCD:  c, J/  survive at T ~1.7T c, Asakawa,Hatsuda,Umeda,….. Relativistic heavy ion collisions Charmonium spectral functions at finite momenta Matsui and Satz, Miyamura… ‘86 Hadron QGP J/  D D D D open charm space-time expansion temperature ~ 200 MeV charmonia ~ 3.0 GeV @ RHIC

13. C.NONAKA KMIIN Charmonia in Heavy Ion Collisions Spectral functions with finite momenta Ill-posed problems correlators on latticespectral functionkernel continuousnoisy, discrete Maximum Entropy Method

14. C.NONAKA KMIIN Bayes’ theorem MEM solution: maximum of Error analysis : essential in MEM analysis Maximum Entropy Method Asakawa, Hatsuda, Nakahara H: all definitions and prior knowledge C: lattice data  2 -likelifood function Shannon-Jaynes entropy m: default model

15. C.NONAKA KMIIN Parameters Actions – standard plaquette action, Wilson fermion – quenched approximation  heavy flavor Lattice sizes – anisotropic lattice:  =a  /a  =4 –  =7.0, a  =9.75×10 -3 fm – large spatial volume: N  X N    X N  P min ~0.5 GeV N t (T/Tc) 96 (0.78) 54(1.3 8) 46 (1.62) 44 (1.70) 42 (1.78) 40 (1.87) 32 (2.33) # of conf.260400 PACS-CS@Tsukuba Blue Gene@KEK  @Nagoya 1000 sweeps between measurementsheat bath : overrelaxation=1:4 Asakawa and Hatsuda, PRL

16. C.NONAKA KMIIN  c at T=0.78Tc N t (T/Tc) 96 (0.78) 54(1.3 8) 46 (1.62) 44 (1.70) 42 (1.78) 40 (1.87) 32 (2.33)  =0.08285  c The first peak ~ 2.9(2)GeV Consistent with experimental value Other structure: lattice artifact

17. C.NONAKA KMIIN  c at T=0.78Tc N t (T/Tc) 96 (0.78) 54(1.3 8) 46 (1.62) 44 (1.70) 42 (1.78) 40 (1.87) 32 (2.33)

18. C.NONAKA KMIIN  c at T=0.78Tc N t (T/Tc) 96 (0.78) 54(1.3 8) 46 (1.62) 44 (1.70) 42 (1.78) 40 (1.87) 32 (2.33)

19. C.NONAKA KMIIN  c at T=0.78Tc N t (T/Tc) 96 (0.78) 54(1.3 8) 46 (1.62) 44 (1.70) 42 (1.78) 40 (1.87) 32 (2.33)

20. C.NONAKA KMIIN  c at T=0.78Tc N t (T/Tc) 96 (0.78) 54(1.3 8) 46 (1.62) 44 (1.70) 42 (1.78) 40 (1.87) 32 (2.33)

21. C.NONAKA KMIIN  c at T=0.78Tc N t (T/Tc) 96 (0.78) 54(1.3 8) 46 (1.62) 44 (1.70) 42 (1.78) 40 (1.87) 32 (2.33)

22. C.NONAKA KMIIN Melting Temperature N t (T/Tc) 96 (0.78) 54(1.3 8) 46 (1.62) 44 (1.70) 42 (1.78) 40 (1.87) 32 (2.33)  c melts between T=1.62 Tc and T=1.70 Tc.

23. C.NONAKA KMIIN Check List MEM: statistical analyses Error analyses Nt dependence Default model dependence

24. C.NONAKA KMIIN Error Analyses N t (T/Tc) 96 (0.78) 54(1.3 8) 46 (1.62) 44 (1.70) 42 (1.78) 40 (1.87) 32 (2.33)  c melts between T=1.62 Tc and T=1.70 Tc.

25. C.NONAKA KMIIN Nt Dependence 33 max. 39 correlator MEM

26. C.NONAKA KMIIN Nt Dependence Large Nt: strong and clear signal Average value of  is almost the same. Smaller Nt calculation has larger error. The shape of spectrum itself changes. Enough number of Nt is indispensable for reliable MEM analyses. 1st peak

27. C.NONAKA KMIIN Default Model Dependence m 0 ＝ 1.15 PQCD (  >>1 GeV) Nt=39

28. C.NONAKA KMIIN Default Model Dependence 2nd,3rd peaks: lattice artifact 1st peak: Error bars suggest that m 0 is the best choice.

29. C.NONAKA KMIIN Check List MEM: statistical analyses Error analyses Nt dependence Default model dependence

30. C.NONAKA KMIIN Temperature Dependence of  N t (T/Tc) 96 (0.78) 54(1.3 8) 46 (1.62) 44 (1.70) 42 (1.78) 40 (1.87) 32 (2.33) The mass of  c increases with temperature. 0 5 10 15 20 25 30  (GeV) Asakawa and Hatsuda, PRL

31. C.NONAKA KMIIN Spectral functions at P≠0 (T=1.62Tc) Qualitatively the shape of spectra functions at p≠0 is almost the same. P min ~0.5 GeV N t (T/Tc) 96 (0.78) 54(1.3 8) 46 (1.62) 44 (1.70) 42 (1.78) 40 (1.87) 32 (2.33)

32. C.NONAKA KMIIN 1st peak at finite momenta  c is stable even at higher momentum. The strength of the peak becomes smaller at higher momentum. The peak shifts to larger  at high momentum. T=1.62Tc

33. C.NONAKA KMIIN Dispersion Relations at T<T c free bosons: The dispersion relation at T=0.78Tc on the lattice is consistent with that of vacuum. P min ~0.5 GeV T=0.78Tc

34. C.NONAKA KMIIN Dispersion Relation @T=1.62Tc p=1 The deviation from dispersion relation at vacuum starts to appear around p~3.0 GeV.  medium effect different from dispersion relation at T<T c p=6 p=7p=8 free bosons:

35. C.NONAKA KMIIN Summary The QCD phase diagram in relativistic heavy ion collisions Phenomenological analyses – Construction of a realistic dynamical model Lattice QCD: heavy flavor – MEM analyses check Error analyses Nt dependence Default model dependence –  c (PS channel) at P=0  c melts between T=1.62 Tc and T=1.70 Tc Mass of  c increases with temperature (T < 1.7 Tc) –  c at finite momenta At T=1.62 Tc medium effects appears in dispersion relations