Thermal radiation from QGP and Lattice QCD Péter Petreczky Nuclear Theory Group and RIKEN-BNL Physics Department Brookhaven National Laboratory

Production rate of thermal photons and dileptos spectral functions

Lattice QCD calculations Current-current correlator in Eucledian time

Motivations : coupling constant is large close to but even at very hightemperatures non-perturbative effects are important at the momentum scale

RHIC II Workshop, BNL, April 29-30, 2005

MEM),,( TpG ),,( Tp

Meson correlators and spectral functions

)(),( iDTG

0 ))2/(sinh(

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

LQCD

),(),(Im12

),(),( ppDpDpDR

Thermal dilepton rate: Thermal photon rate:

McLerran, Toimela, PRD 31 (85) 545

Lattice setup

Karsch, Laermann, Petreczky, Stickan, Wetzorke, PLB 530 (02) 147Non-perturbatively impr. Wilson action

Isotropic Lattice Anisotropic Lattice

space

time

space

Asakasa, Hatsuda, Nakahara,NPA 715 (03) 863 Std. Wilson action

Quenched QCD with Wilson fermions

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

Likelihood function Shannon-Janes entropy:

- default model -perturbation theory

Numerical results on the correlator of the vector currents

constraints on the spectral functions at small energies

Lattice spacing dependence is small !

Karsch, Laermann, Petreczky, Stickan, Wetzorke, PLB 530 (02) 147

Vector spectral functions above deconfinement

Asakasa, Hatsuda, Nakahara,NPA 715 (03) 863

??

Mesons below lattice artifacts

Spectral function and thermal dilepton rate

suppression of low mass dileptons

in sharp contradiction with perturbative expectations predicting enhancement at low energyBraaten, Pisarski, Yuan, PRL 64 (90) 2242

Karsch, Laermann, Petreczky, Stickan, Wetzorke, PLB 530 (02) 147

Spectral functions at finite momenta

Removing lattice artifacts in the spectral functions

Free spectral functions

Wilson fermions Highly improved (HYP) fermions

Removing lattice artifacts in the spectral functions

Free spectral functions

Wilson fermions Highly improved (HYP) fermions

Karsch, Laermann, Petreczky, Stickan, Phys. Rev. D68 (03) 014504

Summary

• Lattice calculations of the vector current correlators together with MEM can provide some informations about thermal radiation

• Current calculations suggest suppression of low mass thermal dileptons compared to the naïve perturbative predictions and possibly very small photon rate

• Lattice artifacts in these calculations are a problem; they areunder control at the level of the correlation functions but needto be understood in the spectal functions => highly improved actions