1. Quarkonia correlators and spectral functions Péter Petreczky Physics Department and RIKEN-BNL SQM 2006, March 26-31, 2006 Meson spectral functions and MEM Lattice calculation of charmonium correlators and spectral functions Lattice calculation of bottomonium correlators and spectral functions Relation of the quarkonium correlators to the heavy quark transport Conclusions and Outlook

2. 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 ?

3. 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

4. Heavy quarkonia spectral functions Isotropic Lattice Anisotropic Lattice space time space Datta, Karsch, P.P. Wetzorke Umeda et al, Asakawa, Hatsuda, Jakovác, P.P, Petrov, Velytsky

5. Charmonia spectral functions at T=0 Jakovác, P.P., Petrov, Velytsky, work in progress For the spectral function is sensitive to lattice cut-off ; In the SC channel even the ground state is poorly resolved ;

6. Charmonia correlators spectral functions at T>0 1S ( ) exists at 1P ( ) is dissolved at Datta, Karsch, P.P, Wetzorke, PRD 69 (2004) 094507 G(T)/G(T=0)=1 Correlators do not agree with potential model with screening ! (see talk by Á. Mócsy )

7. Charmonia correlators: models vs. lattice Lattice data : Datta, Karsch, P.P, Wetzorke, PRD 69 (2004) 094507 Potential model with screening : Á. Mócsy, P.P, hep-ph/0512156 Potential model with screening does not agree with lattice data !

8. Charmonia spectral functions at T>0 from anisotropic lattice no temperature dependence in the PS spectral functions within errors Jakovác, P.P., Petrov, Velytsky, work in progress 1P state is melted See poster by A. Velytsky at SQM 2006, on Thursday, March 30, 2006

9. 1S states are dissolved only at : 1P states are dissolved at : Bottomonia spectral functions on anisotropic lattices expected survive till Jakovác, P.P., Petrov, Velytsky, hep-lat/0509138

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

11. Transport contribution to the Euclidean correlators P.P. and D. Teaney, PRD 73 (06) 014508 Lattice data ( Datta et al, ) :

12. Conclusions 1S charmonia states ( ) survive till unexpectedly high temperatures indications for melting of 1P charmonia states ( ) indications for melting of 1P bottomonia states ( ) Unexpected ! The temperature dependence of the correlators and the spectral functions is inconsistent with screening and potential models ( see talk by Á. Mócsy ) Euclidean correlators calculated on the lattice are sensitive to transport contribution to the spectral functions Better lattice data are required but no indication for DT<1 from the current lattice data

13. Charmonia spectral functions at T=0 (cont’d) Reconstruction of an input spectral function :Lattice data in PS channel for:

14. Removing lattice artifacts in the spectral functions Free spectral functions Wilson fermionsHighly improved ( HYP ) fermions