QCD thermodynamics on the lattice P é ter Petreczky Physics Department and RIKEN-B

1. QCD thermodynamics on the lattice Péter Petreczky Physics Department and RIKEN-BNL • Transition temperature • EoS and quark number susceptibilities • Comparison with resonance gas model • Screening of static quarks at high temperature • Lattice calculation of quarkonium correlators and spectral functions • Conclusions and Outlook Stong and Electroweak Matter 2006 , May 10-13, 2006

2. QCD Phase diagram at T>0 At which temperature does the transition occur ? What is the nature of transition ? transition is crossover !

3. Lattice QCD at T>0 Improved staggered action: p4fat3, asqtad, stout R-algorithm in the past, now RHMC : Costs at T=0: see poster by M. Cheng at SEWM 06 Costs at T>0:

4. Calculations of the transition temperature with p4fat3 action fat3 link improvement of flavor symmetry next-to-nearest neighbors (p4) rotational symmetry to RBC-Bielefeld collaboration : Karsch, Jung, P.P, Schmidt, Umeda (BNL) Cheng, Christ, Mawhiney (Columbia), Ejiri (Tokyo), Petrov (NBI) Doering, Van der Heide, Kaczmarek, Laermann, Miao (Bielefeld)

5. chiral condensate and Polyakov susceptibility multi-histogram Ferrenberg-Swedsen re-weighting posters by Schmidt and Umeda

6. posters by Schmidt and Umeda

7. Equation of state at high temperatures Karsch, Laermann, Peikert, PLB 478 (00) 447 MILC, PoS LAT2005 (2005) 156 Aoki et at, JHEP 0601 (2006) 089 (impr. flavor symmetry only) improvement of rotational symmetry is essential at high T !

8. Quark number susceptibilities : d.o.fabove deconfinement Allton et al, PRD 71 (2005) 054508 Bielefeld-Swansea MILC sQGP scenario Liao, Shuryak, PRD 73 (06) 014509PRD 73 Event by event fluctuations at RHIC What are the degrees of freedom above deconfinement, quark and gluon like quasi-particles or more complex objects ?

9. Comparison with resonance gas Karsch et al, EPJC 29 (2003) 549, PLB 571 (2003) 67

10. Free energies of static charges Kaczmarek, Karsch, P.P., Zantow, PLB 543 (02) 41, PRD 70 (04) 074505, hep-lat/0309121 P.P, Petrov, PRD (2004) 054503 see posters by Hübner, Kaczmarek, Zatnow

11. Entropy and internal energies of static charges Kaczmarek, Zatnow, hep-lat/0506019 P.P, Petrov, PRD (2004) 054503 gauge invariant non-perturbative estimate of the Debye mass Hübner, Kaczmarek, Karsch, P.P, Zatnow Hübner, Kaczmarek, Karsch, P.P, Zatnow

12. Heavy quarkonia spectral functions MEM Isotropic Lattice: Anisotropic Lattice Umeda et al, Eur. Phys. J. C39S1 (2005) 9 Datta et al, PRD 69 (2004) 094507 Asakawa, Hatsuda, PRL 92 (2004) 012001 Jakovac et al, hep-lat/060300

13. PS charmonia spectral functions at finite temperature Datta et al, PRD 69 (2004) 094507 Jakovac et al, hep-lat/060300 extended sources Umeda et al, EPJ C39S1 (05) 9 Asakawa, Hatsuda, PRL 92 (2004) 012001

14. Charmonia correlators spectral functions at T>0 comparison with models : Mócsy, P.P, PRD 73 (06) 074007, poster Datta et al, PRD 69 (2004) 094507 Jakovac et al, hep-lat/060300

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

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

17. Summary and Conclusions • With the help of Teraflop computers lattice calculation of the transition • temperature and EoS are approaching the continuum limit, • but still long way to go • The study of Wilson line correlators can help to better understand screening • at high temperatures:screening entropy produced by static charge • Lessons from heavy quarkonia correlators : • 1S charmonia states ( ) survive till unexpectedly high temperatures • indications for melting of 1P charmonia states ( ) • Euclidean correlators calculated on the lattice are sensitive to transport • contribution in the spectral functions but extracting transport coefficients is • very hard !