1. Lattice QCD at finite temperature Péter Petreczky Physics Department and RIKEN-BNL Winter Workshop on Nuclear Dynamics, March 12-18, 2006 Bulk thermodynamics Static quarks at finite temperature Lattice calculation of quarkonium correlators and spectral functions Relation of the quarkonium correlators to the heavy quark transport Light meson correlators and spectral functions Conclusions and Outlook

2. Equation of state and the transition temperature Karsch, Laermann, Peikert, PLB 478 (00) 447

3. Quark number susceptibilities : d.o.f above deconfinement What are the degrees of freedom above deconfinement, quark and gluon like quasi- particles or more complex object s ? Event by event fluctuations at RHIC Allton et al, PRD 71 (2005) 054508 Bielefeld-Swansea

4. Quark number susceptibilities : lattice data versus sQGP sQGP scenario Liao, Shuryak, PRD 73 (06) 014509 significant contribution from qg, qq bound states and baryons Ejiri, Karsch, Redlich PLB 633 (06) 275 the model qq bound states over predicts the lattice data by factor of two see also Koch, Majumder, Randrup, PRL 95 (2005) 182301

5. Quark number susceptibilities : lattice versus weak coupling J.-P. Blaizot, E. Iancu and A. Rebhan hep-ph/0303185 NLO conventional pertubation theory resummed pertubation theory with quasi-particle masses MILC perturbation theory with dressed quasiparticles can describe the lattice data on the quark number susceptibility lattice data extrapolated to continuum Gavai and Gupta, hep-lat/0211015

6. Free energies of static charges string breaking P.P, Petrov, PRD (2004) 054503 Kaczmarek, Karsch, P.P., Zantow,PRD70 (2004) 074505 We would expect that is dissolved at confinement vacuum physics screening

7. Meson correlators and spectral functions Imaginary time Real time Spectral ( dynamic structure ) function Example : virtual photon quenched approximation is used ! What are the excitations (dof) of the system ?

8. Heavy quarkonia spectral functions Isotropic Lattice Anisotropic Lattice space time space

9. Charmonia spectral functions at T=0 Jakovác, P.P., Petrov, Velytsky, hep-lat/0603005 For the spectral function is sensitive to lattice cut-off ; In the SC channel even the ground state is poorly resolved ;

10. Charmonia correlators spectral functions at T>0 1S ( ) exists at 1P ( ) is dissolved at Datta, Karsch, P.P, Wetzorke, PRD 69 (2004) 094507

11. 1S states are dissolved only at : 1P states are dissolved at : Bottomonia spectral functions on anisotropic lattices expected survive till Jakovác, P.P., Petrov, Velytsky, hep-lat/0509138

12. Vector correlator and heavy quark diffusion Effective Langevin theory Free streaming : Collision less Boltzmann equation 1S charmonium states survies Interactions P.P., Petrov, Velytsky, Teaney, hep-lat/0510021

13. Transport contribution to the Euclidean correlators P.P. and D. Teaney, PRD 73 (2006) 014508 Lattice data ( Datta et al, ) :

14. Light meson spectral function and thermal dilepton rate suppression of low mass dileptons in sharp contradiction with perturbative expectations predicting enhancement at low energy Braaten, Pisarski, Yuan, PRL 64 (90) 2242 Karsch, Laermann, Petreczky, Stickan, Wetzorke, PLB 530 (02) 147

15. Conclusions and Outlook Lessons from heavy quarks : no evidence for “strongly coupled Coulomb phase”, 1S charmonia states ( ) survive till unexpectedly high temperatures indications for melting of 1P charmonia states ( ) indications for melting of 1P bottomonia states ( ) Sequential suppression ? Euclidean correlators calculated on the lattice are sensitive to transport contribution in the spectral functions but extracting transport coefficients is very hard ! Light meson correlators and idence spectral functions: no evidence for bound states suppression of low mass dilepton rate (artifact, generation quasi-particle masses ?) Bulk thermodynamic observables (energy density, susceptibilities, pressure): suggest that dominant degrees of freedom are quarks and gluons for perturbation therory can account for apparent deviation from free gas limit for sQGP models are inconsistent with lattice data

16. Reconstruction of the spectral functions : MEM 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 : - default model - perturbation theory

17. Charmonia spectral functions in PS channel at T>0 ground state peak is shifted, excited states are not resolved when become small no temperature dependence in the PS spectral functions within errors Jakovác, P.P., Petrov, Velytsky, work in progress