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QCD Thermodynamics on Lattice Peter Petreczky

QCD Thermodynamics on Lattice Peter Petreczky Brookhaven National Laboratory. 1. Bulk QCD thermodynamics. Transition and EOS at T>0 QCD at T>0, mu>0 Deconfinement vs. chiral transition in QCD comparison with resonance gas model.

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QCD Thermodynamics on Lattice Peter Petreczky

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  1. QCD Thermodynamics on Lattice Peter Petreczky Brookhaven National Laboratory 1. Bulk QCD thermodynamics • 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.) • 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: Bielefeld, Coulombia, CP-PACS, MILC Physical point: (HPQCD, MILC, UKQCD ) hep-lat/0405022 Chiral extrapolation of With impr. KS fermions: Bielefeld, 2000, p4 action, NPB 605(2001) 579 MILC, 2004, Asqtad action, hep-lat/0405029 MILC, impr. KS Impr. Wilson fermions: CP-PACS PRD 63 (2001) 034502 Nakamura, Latttice 2004 Transition in “real” QCD is most likely a rapid crossover Fodor and Katz, std. KS, JHEP 0404 (2004) 050 Staggered and Wilson fermions violate flavor symmetries of QCD !!

  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 1st order transition in Nf=2 QCD ? Carmona et al., hep-lat/0309035, Di Giacomo, Lattice ‘ 04, Pica, Lattice ‘04 Standard staggered action However, 1st 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 MILC Coll. Transition gets smoother on finer lattices, imrovement of flavor symmetry ? HYP staggered fermions at Nt=4 -> Hasenfratz, Knechtli, hep-lat/0202019

  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: See talk by Ejiri, Lattice 2004 Crossover Phase transition 2001: Fodor, Katz, JHEP 0203 (2002) 014 Lattices:

  10. Fodor, Katz, JHEP 0404 (2004) 050 2004: crossover 1st order de Forcrand, Philipsen Fodor, Katz Comparison with analytic continuation

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

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

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

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

  16. Quark number susceptibilities See talk by Ejiri

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

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

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

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

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

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

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

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

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

  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, 2nd and 3rd 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 Datta, Karsch, P.P, Wetzorke, PRD 69 (2004) 094507 1/a=4.86GeV 1/a=9.72GeV 1/a=4.04GeV Lattice artifacts !!! 2nd and 3rd peaks are lattice artfifacts, no 2S state

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

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

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

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

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

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

  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 • 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) • 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 !!!

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