1. Heavy quarks in finite temperature lattice QCD Péter Petreczky Physics Department and RIKEN-BNL Exploring QCD : Deconfinement etc, Newton Institute, Cambridge, August 20-24, 2007 Introduction : Deconfinement at high temperature and color screening Free energy of static quarks in 2+1 F QCD Quarkonium correlators and spectral functions from lattice Heavy quark transport and quarkonia correlators Conclusions and Outlook

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

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

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

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 : - default model - perturbation theory

8. 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

9. If there is no T-dependence in the spectral function, temperature dependene of Charmonia correlators at T>0 in agreement with previous quenched calculations: Datta et al, PRD 69 (04) 094507 Jakovác, P.P., Petrov, Velytsky, PRD 75 (07) 014506 very similar results in full (2 F) QCD : Aarts et al, arXiv:0705.2198

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

11. 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

12. Charmonia spectral functions at T>0 (cont’d)

13. Can 1S charmonia state survive deconfinement ? resonance-like structures disappear already by 1.2Tc strong threshold enhancement contradicts lattice results ? resonance-like structures disappear already by 1.2Tc strong threshold enhancement contradicts lattice results ?  higher excited states gone  continuum shifted  1S becomes a threshold enhancement Mócsy, P. P., arXiV:0705.2559 [hep-ph] cc What about color screening ? No !

14. >> deconfinedconfined charm 1.5 Tc bottom 1.5 Tc Scalar and axial-vector correlators free theory: quasi-free charm (beauty) carriers see also Umeda PRD 75 (07) 094502

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

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

17. 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, the same is true for the derivative of the correlator in the SC channel. MEM is not a reliable tool for extracting the spectral functions at high temperatures Potential model with screening leads to the dissolution of most quarkonia states above deconfinement, nevertheless are compatible with lattice data on quarkonium correlators => large threshold enhancement The observed temperature dependence of the quarkonium correlators is governed by the transport contribution (zero mode contribution) not by threshold (resonance) region of the spectral functions small thermal velocity of charm quarks lattice data are not precise yet to constrain the value of heavy quark diffusion constant D

18. Back-up slide