The QCD Phase Diagram in Relativistic Heavy Ion Collisions October 24, Inauguration Conference Chiho NONAKA, Nagoya University

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

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…

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

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

C.NONAKA KMIIN Nonaka and Bass PRC75:014902(2007) Highlights of 3D

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

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 (2003) R.J. Fries, C. Nonaka, B. Mueller & S.A. Bass, PRC (2003) C. Nonaka, R.J. Fries & S.A. Bass, Phys. Lett. B (2004) C. Nonaka, B. Mueller, M. Asakawa, S.A. Bass & R.J. Fries, PRC (2004)

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

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

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

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 RHIC

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

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

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 Blue 1000 sweeps between measurementsheat bath : overrelaxation=1:4 Asakawa and Hatsuda, PRL

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)  =  c The first peak ~ 2.9(2)GeV Consistent with experimental value Other structure: lattice artifact

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)

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)

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)

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)

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)

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.

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

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.

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

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

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

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

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

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  (GeV) Asakawa and Hatsuda, PRL

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)

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

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

C.NONAKA KMIIN Dispersion 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:

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