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Heavy quarks in finite temperature lattice QCD P é ter Petreczky

Heavy quarks in finite temperature lattice QCD P é ter Petreczky Physics Department and RIKEN-BNL. Introduction : Deconfinement at high temperature and color screening Free energy of static quarks

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Heavy quarks in finite temperature lattice QCD P é ter Petreczky

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  1. Heavy quarks in finite temperature lattice QCD Péter Petreczky Physics Department and RIKEN-BNL • Introduction : Deconfinement at high temperature and color screening • Free energy of static quarks • Quarkonium correlators and spectral functions from lattice • Heavy quark transport and quarkonia correlators • Conclusions and Outlook AGS & RHIC User’s Metting, June 20, 2007

  2. Deconfinement at high temperatures RBC-Bielefeld collaboration (preliminary) large increase in number of d.o.f. chromo-electric screening bindings effects in quarkonium are reduced ( Matsui and Satz ) study spatial correlators of static color charges in LQCD at T>0 potential model lattice calculations of quarkonium spectral functions in LQCD

  3. 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

  4. Static quark anti-quark free energy in 2+1f QCD RBC-Bielefeld Collaboration: M. Cheng, N.H. Christ, S. Eijiri, K. Hübner, C. Jung, F., O. Kaczmarek, F. Karsch, E. Laermann, J. Liddle, R. Mawhinney, C. Miao, P. Petreczky, K. Petrov, C. Schmidt, W. Söldner, J. Van der Heide preliminary preliminary

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

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

  7. 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: -perturbation theory - default model

  8. Lattice results on charmonium spectral functions 1S charmonium survives deconfinement : This seemingly contradicts to large color screening of static charges ! Umeda et al, EPJ C39S1 (05) 9 Asakawa, Hatsuda, PRL 92 (04) 012001 Datta et al, PRD 69 (04) 094507 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 Are potential model applicable at T>0 ? Mócsy, P.P., PRD 73 (06) 074007 more recently confirmed by : Iida et al, PRD74 (06) 074502 Aarts et al, arXiv:0705.2198 [hep-lat] New high statistics with careful analysis of systematic errors: Jakovác, P.P., Petrov, Velytsky, PRD 75 (07) 014506

  9. 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

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

  11. Bottomonium correlators Jakovác, P.P., Petrov, Velytsky, PRD 75 (07) 014506

  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. Using default model from the high energy part of the T=0 spectral functions : resonances appears as small structures on top of the continuum, almost no T-dependence in the PS spectral functions till Jakovác, P.P., Petrov, Velytsky, PRD 75 (07) 014506

  14. 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

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

  16. Conclusions • Lattice QCD study of free energy of static color charges shows strong color • screening at distances comparable to quarkonium sizes • Quarkonium correlation functions in the PS channel show only very small • temperature dependence, but large enhancement of the correlation functions • over the T=0 results is seen in the SC channel • S-wave charmonium spectral are temperature independent within errors but • the details of the spectral functions (e.g. presence of resonance peaks) cannot • be resolved yet • Transport contribution to quarkonium correlators has be isolated • small thermal velocity of charm quarks • lattice data are not precise yet to constrain the value of heavy quark • diffusion constant D

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