Lattice QCD at finite temperature Péter Petreczky Nuclear Theory Group and RIKEN-BNL Brookhaven National Laboratory QCD Thermodynamics on the lattice Bulk Thermodynamics: Nature of transition to the “new state”, transition temperature, Equation of state Chiral and quark number suscpetibilities Spatial and temporal correlators: Free energy of static quarks ( potential ) Heavy quarkonia correlators and spectral functions Light meson correlators (dilepton rate) Quark and gluon propagators and quasi-particle masses 40th Recontres De Moriond, La Thuile, March, 2005

QCD Phase diagram at T>0 At which temperature does the transition occur ? What is the nature of transition ? Resonance Gas : Chapline et al, PRD 8 (73) 4302 global symmetries of QCD are violated in lattice formulation staggered fermions :

The chiral transition at T>0 2+1F : Petreczky, J. Phys. G30 (2004) S1259

The chiral susceptibility at T>0 Improved stagg., asqtad, MILC, hep-lat/0405029 Improved stagg. HYP: better flavor symmetry at finite lattice spacing

Equation of state at T>0 Requirements: for lattice Computational cost grow as : Karsch et al, EPJC 29 (2003) 549, PLB 571 (2003) 67

Static quark anti-quark pair in T>0 QCD QCD partition function in the presence of static pair McLerran, Svetitsky, PRD 24 (1981) 450 temporal Wilson line: Polyakov loop: = - r

Separate singlet and octet contributions using projection operators Nadkarni, PRD 34 (1986) 3904 Color singlet free energy: Color octet free energy: Color averaged free energy:

Free energies of static charges in absence dynamical quarks: Kaczmarek, Karsch, Petreczky, Zantow, hep-lat/0309121 confinement, sr deconfinement => screening Vacuum (T=0) physics at short distances

Running coupling constant at finite temperature Effective running coupling constant at short distances : T=0 non-perturbative physics Perturbation theory: Kaczmarek, Karsch, P.P., Zantow, Phys.Rev.D70 (2004) 074505 T-dependence 3-loop running coupling Necco, Sommer, NPB 622 (02)328

Free energies of static charges in full QCD string breaking Petreczky, Petrov, PRD (2004) 054503 screening Vacuum physics

Entropy and internal energies of static charges resonace gas ?

Schroedinger equation : 1S charmonia states survive up to Quenched QCD : Kaczmarek, Karsch, Petreczky, Zantow, hep-lat/0309121 Schroedinger equation : 1S charmonia states survive up to Shuryak, Zahed, hep-ph/0403127, Wong, hep-ph/0408020

Meson correlators and spectral functions Experiment, dilepton rate LGT Imaginary time Real time Quasi-particle masses and width KMS condition MEM

Heavy quarkonia spectral functions Isotropic Lattice Anisotropic Lattice time space space Jakovác, P.P.,Petrov, Velytsky, in progress Fermilab action, also Asakawa, Hatsuda, PRL 92 (04) 012001 Umeda et al, hep-lat/0211003 Datta, Karsch, Petreczky, Wetzorke, PRD 69 (2004) 094507 Non-perturbatively impr. Wilson action

Charmonia spectral functions at T=0 Jakovác, P.P.,Petrov, Velytsky, work in progress, calculation on 1st QCDOC prototype Lattice artifacts by K. Jansen FAQ: Could it be that also the 1st peak is a lattice artifact Answer: NO

Charmonia spectral functions on isotropic lattice Heavy quarkonia spectral functions from MEM : Datta, Karsch, Petreczky, Wetzorke, PRD 69 (2004) 094507 1S ( ) is dissolved at 1P ( ) is dissolved at 1S state was found to be bound till also in Umeda et al, hep-lat/0211003 Asakawa, Hatsuda, PRL 92 (04) 012001

Charmonia at finite temperature on anisotropic lattice Jakovác, P.P.,Petrov, Velystksy, work in progress

Summary In “real” QCD the transition seems to be crossover not a true phase transition. Chiral aspect of the transition strongly depends on the effects of finite lattice spacing ; no evidence for chiral transition from the lattice yet ! Bulk thermodynamic quantities below and in the vicinity of are well described by hadron resonance gas model The interactions between quarks remains non-perturbative above deconfinement transition but no evidence for “extraordinary” large coupling 1S charmonia, can exist in the plasma as resonance up to temperatures 1P charmonia dissolve at

Charmonia correlators at T>0 on isotropic lattice If spectral function do not change across :

spectral function at high energy is not described by the free theory, What is the physics behind the 2nd and 3rd peaks ? Lattice spectral functions in the free theory, Karsch, Laerman, Petreczky, Stickan, PRD 68 (2003) 034008 spectral function at high energy is not described by the free theory, 2nd and 3rd peaks are part of distorted continuum. Finite lattice spacing effects are small in the correlator and their size is in accordance with expectations from the free field theory limit.

Reconstruction of the spectral functions data and degrees of freedom to reconstruct Bayesian techniques: find which maximizes data Prior knowledge Maximum Entropy Method (MEM) Asakawa, Hatsuda, Nakahara, PRD 60 (99) 091503, Prog. Part. Nucl. Phys. 46 (01) 459 Likelyhood function Shannon-Janes entropy: -perturbation theory - default model