1. Recent developments in lattice QCD Péter Petreczky Physics Department and RIKEN-BNL Early time dynamics in Heavy Ion Collisions, McGill University, Montréal, July 16-19, 2007 Thermodynamics of 2+1 flavor QCD for nearly physical quark masses 1.Equation of State 2.Quark number and strangeness fluctuations 3.Color screening at high temperatures Quarkonium correlators 1.Quarkonium properties at T>0 2.Transport contribution to quarkonium correlators Conclusions

2. Lattice calculations with p4fat3 action fat3 link improvement of flavor symmetry next-to-nearest neighbors (p4) rotational symmetry to RBC-Bielefeld collaboration : Ejiri, Karsch, Jung, P.P, Schmidt, Umeda (BNL) Cheng, Christ, Mawhiney (Columbia), Datta (Mumbai), Petrov (NBI) Doering, Van der Heide, Kaczmarek, Laermann, Miao (Bielefeld) RHMC algorithm : x 20 speedup at small m

3. Equation of State Calculations :, and lattices, and along the line of constant physics ( LCP ) : are varied in the way physical quantities, e.g. and

4. Equation of State (cont’d) rise in the entropy and energy density happens in the same temperature interval where the rapid change of the chiral condensate and Polyakov loop takes place no large cutoff dependence in the pressure and entropy denisty deviation from ideal gas limit is about 10% at high T

5. Equation of State (cont’d) (2+1) flavor QCD Resummed perturbative calculations from : Blaizot, Iancu, Rebhan, hep-ph/0303185 Lattice data on pressure and entropy density at high temperatures can be described by re-summed perturbation theory qualitative agreement with resonance gas at low T

6. Quark number and strangeness fluctuations

7. Static quark anti-quark free energy in 2+1f QCD preliminary

8. Static quark anti-quark free energy in 2+1f QCD preliminary

9. Lattice results on charmonium spectral functions Umeda et al, EPJ C39S1 (05) 9 Asakawa, Hatsuda, PRL 92 (04) 012001 Datta et al, PRD 69 (04) 094507 1S charmonium survives deconfinement : more recently confirmed by : Iida et al, PRD74 (06) 074502 Aarts et al, arXiv:0705.2198 [hep-lat] This seemingly contradicts to large color screening of static charges ! No problem lattice results can be reproduced using potential models: Shuryak, Zahed, PRD 70 (04) 054507 Wong, PRC 72 (05) 03496 Alberico et al, PRD 72 (05) 114011 Rapp, Cabrera, hep-ph/0610254 Wong, Crater, PRD 75 (07) 034505 Alberico et al, PRD 75 (07) 074009 New high statistics with careful analysis of systematic errors: Jakovác, P.P., Petrov, Velytsky, PRD 75 (07) 014506 Are potential model applicable at T>0 ? Mócsy, P.P., PRD 73 (06) 074007

10. Charmonia spectral functions at T=0 Jakovác, P.P., Petrov, Velytsky, PRD 75 (07) 014506 For the spectral function is sensitive to lattice cut-off ; Strong default model dependence in the continuum region

11. If there is no T-dependence in the spectral function, temperature dependene of Charmonia correlators at T>0 PSSC in agreement with previous calculations: Datta et al, PRD 69 (04) 094507

12. 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, PRD 75 (07) 014506

13. 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

14. P.P., Teaney PRD73 (06) 014508

15. Summary Pressure, energy density and entropy density have be calculated at two lattice spacing show a rapid rise at temperature in agreement with deviation from the ideal gas limit is about 10% for temperatures and no significant cutoff dependence has been seen Cheng et al, PRD 75 (07) 034506 Fluctuations of quark number and strangeness at high temperatures are close to the ideal gas limit Interactions between static quarks are strongly screened in the quark gluon plasma, the onset of screening is seen at distances comparable to the 1S quarkonium size S-wave charmonium correlators are temperature independent and there is no T-dependence in the reconstructed spectral functions, however, details are not resolved Can 1S charmonia exist in the plasma ? What about color screening ? see talk by Ágnes Mócsy Transport contribution to charmonium correlators have been isolated : small thermal velocity for heavy quarks, no constraint on the diffusion constant

16. Aoki et at, JHEP 0601 (2006) 089 (impr. flavor symmetry only)