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 stateChiral and quark number suscpetibilities

Spatial and temporal correlators:

Free energy of static quarks ( potential ) Heavy quarkonia correlators and spectralfunctionsLight 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

AAV SUUSUSU )3()1()3()3( staggered fermions :

The chiral transition at T>0

Petreczky, J. Phys. G30 (2004) S1259

2+1F :

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

Computational cost grow as :

Requirements: for lattice

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 pairMcLerran, Svetitsky, PRD 24 (1981) 450

temporal Wilson line:

Polyakov loop: )xTr W()( xL

- =

r

Color singlet free energy:

Color octet free energy:

Separate singlet and octet contributions using projection operators

81 and PP Nadkarni, PRD 34 (1986) 3904

8133

Color averaged free energy:

Kaczmarek, Karsch, Petreczky, Zantow, hep-lat/0309121

Free energies of static charges in absence dynamical quarks:

Vacuum (T=0) physics at short distances

confinement, r

deconfinement => screening

Effective running coupling constant at short distances :

Running coupling constant at finite temperature

Perturbation theory:

Kaczmarek, Karsch, P.P., Zantow, Phys.Rev.D70 (2004) 074505

T=0 non-perturbativephysics

T-dependence

3-loop running couplingNecco, Sommer, NPB 622 (02)328

Free energies of static charges in full QCD

fmrJ 44.0/

string breaking

Vacuum physics

screening

Petreczky, Petrov, PRD (2004) 054503

Entropy and internal energies of static charges

resonace gas ?

Quenched QCD :

Kaczmarek, Karsch, Petreczky, Zantow, hep-lat/0309121

Schroedinger equation :1S charmonia states survive up toShuryak, Zahed, hep-ph/0403127, Wong, hep-ph/0408020

),(),(),(,)0,0(),(),,( 3 xqxqxJJxJexdTpG HHHHxpi

MEM),,( TpG ),,( Tp

Meson correlators and spectral functions

5,,5,1H

)(),( iDTG

Imaginary time Real time

0 ))2/(sinh(

))2/(1(cosh(),(),(

T

TTdTG

LGTExperiment, dilepton rate

Quasi-particle masses and width

)()(Im1

2

)()(

RDDD

KMS condition

Heavy quarkonia spectral functions

Datta, Karsch, Petreczky, Wetzorke, PRD 69 (2004) 094507Non-perturbatively impr. Wilson action

Isotropic Lattice Anisotropic Lattice

space

time

space

Jakovác, P.P.,Petrov, Velytsky, in progressFermilab action,

alsoAsakawa, Hatsuda, PRL 92 (04) 012001Umeda et al, hep-lat/0211003

Charmonia spectral functions at T=0

FAQ: Could it be that also the 1st peak is a lattice artifact

Answer: NO

Jakovác, P.P.,Petrov, Velytsky, work in progress,calculation on 1st QCDOC prototype

Lattice artifacts

by K. Jansen

Charmonia spectral functions on isotropic lattice

Heavy quarkonia spectral functions from MEM :

1S ( ) is dissolved at

cT3/J 1P ( ) is dissolved at ccT1.1

Datta, Karsch, Petreczky, Wetzorke, PRD 69 (2004) 094507

1S state was found to be bound till also in Umeda et al, hep-lat/0211003Asakawa, Hatsuda, PRL 92 (04) 012001

cT5.1

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 !

• 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

• Bulk thermodynamic quantities below and in the vicinity of are well described by hadron resonance gas model

Charmonia correlators at T>0 on isotropic lattice

If spectral function do not change across :

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 latticespacing effects are small in the correlator and their size is in accordancewith 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 knowledgeMaximum Entropy Method (MEM)

Asakawa, Hatsuda, Nakahara, PRD 60 (99) 091503, Prog. Part. Nucl. Phys. 46 (01) 459

Likelyhood function Shannon-Janes entropy:

- default model -perturbation theory