Quarkonia at finite temperature: lattice results Peter Petreczky Brookhaven National Laboratory Introduction : Quarkonium dissolution at finite temperature Color screening at finite temperature : lattice results Mesons spectral functions: lattice results Conclusions QWG workshop, Beijing, October 15, 2004

Quarkonium dissolution at finite temperature Potential between singlet pair Coulomb gauge gluon propagator Matsui and Satz, PLB 178 (1986) 416 No quarkonium binding is possible when Charmonium suppresseion right after deconfinement Implicit assumption : instantenous modification of interaction by the medium Does not hold close to

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

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

Free energy in the pertubative high temperature limit at leading order At next to leading order and the entropy appears: The internal energy is different from the free energy

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

The entropy contribution and the internal energy Numerically: Negative entropy contribution 1S charmonia states survive up to Shuryak, Zahed, hep-ph/0403127 Wong, hep-ph/0408020 Kaczmarek, Karsch, P.P., Zantow, hep-lat/0309121

Static free energy in 3 flavor QCD Improved staggered (Asqtad) action, lattices Quark masses: K. Petrov, P.P, hep-lat/0405009 Effective screening radius String breaking screening Vacuum physics

decreases, do D,B meson masses decrease ?? Entropy contribution Digal, P.P. , Satz, PLB 514 (2001) 57 decreases, do D,B meson masses decrease ?? Entropy contribution K. Petrov, P.P, hep-lat/0405009 Large increase in the entropy and internal energy !

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

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: - default model -perturbation theory

Lattice set-up Charmonia : Bottomonia : Non-perturbatively improved Wilson action, isotropic lattices Charmonia : Bottomonia : Anisotropic Fermilab action,

Charmonia spectral functions (I) What do we get at low temperature from lattice calculations ? Calculations performed on isotropic lattices for 1/a=4.04GeV, 4.86GeV,9.72GeV 1/a=4.04GeV 1/a=4.86GeV 1/a=9.72GeV Lattice artifacts by K. Jansen 2nd and 3rd peaks are lattice artfifacts, no 2S state

Charmonia spectral functions (II) 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

Charmonia spectral functions (III) 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 to suppression what is the thermal width ???

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

Temperature dependence of bottomonium correlators No T-dependence as expected for 1S state Little supprise ! Expected: Qualitatively similar T-dependence for different lattice spacings Petrov, Velytsky, P.P, work in progress

Conclusions non-perturbative even in the deconfined phase Interaction between quark and anti quark are strong and non-perturbative even in the deconfined phase The 1P state charmonia dissolve at The lattice data support a picture of gradual dissolution of ground state charmonia starting at and no states are present at 1P bottomonium state dissolve around . What determines the Dissociation temperature quantum numbers or system size ? Future challenge : better control of lattice artifatcs,

Discussions Considerable progress in study of quarknium at finite temperature in lattice QCD but the problem of cut-off effects and systematic errors in MEM is not settled Completely. Better actions (perfect actions, NRQCD for bottomonium) Extension to full QCD. Lattice spacing dependence of

Dependence of the spectral functions on number of data points Resolution problem for bottomonium NRQCD What is the thermal width of quarkonium states ?

Quarkonium formation in the medium : Evidence for very large energy density (jet quenching, hydro, multiplicities ), fast equilibrization (hydro) Quarkonium may be formed inside a high density medium  in-medium quarkonium binding has to be understood. Can be quarkonium used as thermometer ? Experimental input: measure quarkonium production as function of pT and y in AA with pp and dA baseline. Measure chi_b ? To what is extent potential model can be used at T>0 (ok at T=0). Can one calculate reliably the quarkonium width perturbatively ? Wong, hep-ph/0408020