1. QCD Thermodynamics on Lattice Peter Petreczky Brookhaven National Laboratory Transition and EOS at T>0 QCD at T>0, mu>0 Deconfinement vs. chiral transition in QCD comparison with resonance gas model 2. Testing hot QCD with pair (screening, mesons etc.) 1. Bulk QCD thermodynamics Free energy of static quark anti-quark pair Meson spectral function from lattice QCD Quarkonia spectral functions above deconfinement Light meson spectral function above deconfinement

2. Bulk Thermodynamics in SU(3) gauge theory What is the order of the transition ? What is the transition temperature What is the EOS ? Boyd et al., Nucl. Phys. B496 (1996) 167 Necco, Nucl. Phys. B683 (2004) 167 The problem has been “solved” !

3. QCD phase diagram at T>0 Lattice calculations of QCD for physical value of the quark (pion) masses is extremely difficult: Physical point: (HPQCD, MILC, UKQCD ) hep-lat/0405022 Transition in “real” QCD is most likely a rapid crossover Bielefeld, Coulombia, CP-PACS, MILC Staggered and Wilson fermions violate flavor symmetries of QCD !! MILC, impr. KS Fodor and Katz, std. KS, JHEP 0404 (2004) 050 Chiral extrapolation of With impr. KS fermions: Bielefeld, 2000, p4 action, NPB 605(2001) 579 MILC, 2004, Asqtad action, hep-lat/0405029 Impr. Wilson fermions: CP-PACS PRD 63 (2001) 034502 Nakamura, Latttice 2004

4. Finite temperature transition with asqtad action (I) MILC Coll., hep-lat/0405029, hep-lat/0309118, hep-lat/0209079, hep-lat/0110067 Chiral condensate and susceptibility

5. Finite temperature transition with asqtad action (II) Quark number susceptibilities fluctuations of conserved charges SB limit is almost reached at 2Tc Cut-off effects are smaller than in the free theory Nt=6 is already very close to the continuum

6. Is there a 1 st order transition in Nf=2 QCD ? Carmona et al., hep-lat/0309035, Di Giacomo, Lattice ‘ 04, Pica, Lattice ‘04 Standard staggered action However, 1 st transition is also observed for Nf=4 standard staggered action, but for HYP staggered action there is a only a crossover Hasenfratz, Knechtli, hep-lat/0105022

7. Transition in the continuum limit Transition gets smoother on finer lattices, imrovement of flavor symmetry ? HYP staggered fermions at Nt=4 -> Hasenfratz, Knechtli, hep-lat/0202019 MILC Coll.

8. QCD thermodynamics in the presence of finite chemical potential Technical problem: Finite complex action reweighting sign problem, overlap problem: Multi-parameter reweghting, Fodor, Katz Taylor expansion around mu=0, Bielefeld-Swansea Coll. Analytic continuation from imaginary mu, de Focrand, Philipsen; D’Elia, Lombardo See pleanry talk by S. Katz on Lattice 2003, hep-lat/0310051 Physics problem : Interesting phase diagram in the plane If there is a crossover at a chiral Critical end-point exist at some value of the chemical potential, Stephanov, Rajagopal, Shuryak, PRL 81 (98) 4816 Where is the Endpoint ??

9. Locating the critical end-point Multiparameter rewigting: Lee-Yang zeroes: Crossover Phase transition 2001: Fodor, Katz, JHEP 0203 (2002) 014 Lattices: See talk by Ejiri, Lattice 2004

10. 2004: crossover1 st order Fodor, Katz, JHEP 0404 (2004) 050 Comparison with analytic continuation de Forcrand, Philipsen Fodor, Katz

11. Taylor expansion around zero chemical potential and EOS Continuum SB Allton et al., Phys. Rev. D68 (2003) 014507 including n=3, see talk by Ejiri Csikor et al., JHEP 0405 (2004) 046 Multiparameter reweighting:

12. New developments: calculations with fixed baryon number Kratochvila, de Forcrand, Lattice 2004 Alexandru, Lattice 2004 The sign problem is less severe but are this study are feasible For larger volumes ? (currently 4^4)

13. Comparison with resonance gas at low T For fixed the ratio of These observable is T-independent The ratios of the expansion coeffiecients are Compare with LGT results (Bielefeld-Swansea Coll) : Consequences: Karsch, Redlich, Tawfik, PLB 571 (2003) 67 ~1000 Exp. Know resonances

14. Ratios of different quantities: Karsch, Redlich, Tawfik, EPJC 29 (2003) 549, PLB 571 (2003) 67 See talk by Ejirii on Lattice 2004 Bielefeld –Swansea Coll.

15. To predict the temperature dependence of the pressure, susceptibilities we need the quark mass dependence of hadron masses ! Karsch, Redlich, Tawfik, EPJC 29 (2003) 549 ? Reasonable description of lattice data

16. Quark number susceptibilities See talk by Ejiri

17. What drives the transition in QCD ? Deconfinement vs. chiral transition for all Karsch, Redlich, Tawfik, EPJC 29 (2003) 549 Role of hadron resonances ? Though depends on The deconfinement transition is driven resonances (energy density) !

18. Testing hot QCD matter with quark anti-quark pair Static quark anti-quark pair  heavy quark potentials All started with McLerran and Svetitsky, PRD 24 (1981) 450 Matsui and Satz, PLB 178 (1986) 416 Time scales: 1/T < t < Heavy quark anti-quark pair  heavy quarkonia spectral functions Time scales: 1/m < t< 1/mv Light quark anti-quark pair  light meson spectral functions Time scales: t~1/T Heavy quarkonia and open charm physics at T>0 Heavy quarkonia physics at T>0 Thermal dilepton and photons, mesons What is the range of interaction and what is g(T) ?

19. Static quark anti-quark pair in T>0 QCD QCD partition function in the presence of static pair McLerran, Svetitsky, PRD 24 (1981) 450 temporal Wilson line: Polyakov loop: Separate singlet and octet contributions using projection operators Nadkarni, PRD 34 (1986) 3904

20. Color singlet free energy: Color octet free energy: Fix the Coulomb gauge transfer matrix can be defined Dressed gauge invariant Wilson line Philipsen, PLB 535 (2002) 138 equivalent At T=0 equivalent to definition through Wilson loop, Philipsen, PLB 535 (2002) 138

21. Color averaged free energy: Vacuum (T=0) physics, short distances rT<<1 Linear rise : Screening : long distances rT>>1 Singlet contribution is dominant for rT<<1 T ln 9 Kaczmarek, Karsch, P.P., Zantow, hep-lat/0309121

22. Effective running coupling constant at short distances : Short vs. long distance physics in singlet free energy 3-loop running coupling Necco, Sommer, NPB 622 (02)328 T-dependence Perturbation theory: Kaczmarek, Karsch, P.P., Zantow, hep-lat/0406036 T=0 non-perturbative physics

23. Screening at large distances: High temperature perturbation theory: The only non-perturbative information Kaczmarek, Karsch, P.P., Zantow, hep-lat/0406036

24. The entropy contribution and the internal energy Negative entropy contribution Numerically: Kaczmarek, Karsch, P.P., Zantow, hep-lat/0309121

25. Static free energy in full QCD Petrov, Lattice 2004, Petrov, P.P, hep-lat/0405009 String breaking screening Effective screening radius Vacuum physics 3 flavor QCD, asqtad action, 2 flavor QCD, p4 action Kaczmarek et al., hep-lat/0312015 2+1 flavor QCD std. KS study extended to finite denisty Toth, Katz, Fodor Lattice 2004 decreases with increasing

26. Large increase in the entropy and internal energy due to inclusion of a static meson ! Large decrease in large increase in Similar increase also observed if an extra baryon is include in the system Kratochvila, Lattice 2004

27. MEM Meson correlators and spectral functions Imaginary time Real time LGT Experiment, dilepton rate Quasi-particle masses and width KMS condition

28. Reconstruction of the spectral functions 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 : Other methods: S. Gupta, hep-lat/0301006 G.P. Lepage et al., hep-lat/0110175 Constrained curve fitting - default model - perturbation theory

29. Cutoff effects in the spectral function Does the integral represenation of the imaginary time correlator holds on the lattice ? How the cutoff effects in manifest themselves in ? Asymptotic freedom analyze cutoff effects in in the free theory Karsch, Laermann, P.P, Stickan, PRD 68 (2003) 014504 For Wilson action on anisotropic lattice Cutoff effects are entirely contained in

30. Wilson action : Large cutoff effects Move away as Truncated FP action : Bietenholz, NPB PS 53 (97 ) 921 Large reduction of the cutoff effects

31. Meson spectral functions at T=0 CP-PACS, Yamazaki et al, PRD 65 (2002) 014501 No continuum only peaks, 2 nd and 3 rd peak scale like 1/a ! This happens not only for Wilson action, see poster by Blum, P.P, Latttice’ 04

32. Heavy quarkonia spectral functions (I) Asakawa, Hatsuda, PRL 92 (2004) 012001 Wilson action, anisotropic lattices, Datta, Karsch, P.P, Wetzorke, PRD 69 (2004) 094507 Non-perturbativel impr. Wilson action, isotropic lattices, Umeda, Nomura, Matsufuru, hep-lat/0211003 Fermilab action, anisotropic lattices,, extended operators

33. Heavy quarkonia spectral functions (II) What do we get at low temperature from lattice calculations ? Calculations performed on isotropic lattices for 1/a=4.04GeV, 4.86GeV, 9.72GeV Lattice artifacts !!! 1/a=4.04GeV 1/a=4.86GeV 1/a=9.72GeV 2 nd and 3 rd peaks are lattice artfifacts, no 2S state Datta, Karsch, P.P, Wetzorke, PRD 69 (2004) 094507

34. Heavy quarkonia spectral functions (III) The temperature dependence of the correlators If there is no T-dependence in the spectral function, x x Datta, Karsch, P.P., Wetzorke, PRD 69 (2004) 094507

35. Heavy quarkonia spectral functions (IV) Heavy quarkonia spectral functions from MEM: Gradual dissolution of ; screening cannot lead to suppression what is the thermal width ??? is dissolved at Is dissolved at Datta, Karsch, P.P., Wetzorke, PRD 69 (2004) 094507

36. Results from anisotropic lattices: Asakawa, Hatsuda, PRL 92 (2004) 012001 Point operators Umeda, Nomura, Matsufuru, Lattice 2004, Smeared operators

37. Light meson spectral functions (I) Asakawa, Hatsuda, Nakahara, Nucl.Phys. A715 (2003) 863 No light mesons are expected to exist above deconfinement temperatures ! Anisotropic lattices: Std. Wilson fermions Meson resonance above deconfinement ! Approximate degeneracy of PS, SC, V, AV channels !

38. Light meson spectral functions (II) Large deviation from 1 Scaling with T Karsch, Laermann, P.P.,Stickan, Wetzorke, Nucl.Phys. A715 (2003) 701 work in progress Lattice artifacts ! Isotropic lattices : fixed by NP clover fermions,

39. Vector spectral functions and thermal dilepton rate: Mesons below Strong correlations above ?? Suppression of low mass dileptons above Karsch, Laermann, P.P.,Stickan, Wetzorke, PLB 530 (2002) 147, work in progress Light meson spectral functions (III)

40. Summary There is most likely no phase transition but rapid crossover in full QCD, Improvement of flavor symmetry in the staggered fermion formulation may have a large impact on the phase transition Strong interaction between quarks in the deconfined phase: (though bulk quantities suggest a nearly free gas of quarks and gluons) non-perturbative behavior of the static quark anti-quark free energy, large value of in the deconfined phase. survival of Existence of “meson resonances” in the deconfined phase suppression of low mass dileptons this is sQGP as seen on lattice !!! There is a substantial progress at finite, but we are far from final results, need the continuum limit Lattice data provide evidence for Hagedorn type transition in full QCD (a density driven deconfinement transition)