Overview of Potential models at finite temperature Péter Petreczky Physics Department and RIKEN-BNL Brief history : Potential models with screening and quarkonium dissociation in the quark gluon plasma (1986-2003): J/psi melts at T<1.2Tc, Upsilon melts at T~2Tc, excited charmonium states melt around Tc (Matsui, Satz, 1986, ….) Lattice calculations of quarkonium correlators and spectral functions (2003-2006): J/psi survives till T~1.6Tc, Upsilon does not melt, excited charmonium states melt around Tc (Umeda 2002, Asakawa, Hatsuda, 2003, Datta et al, 2003) Role of zero mode contribution and threshold enhancement (2006-2008) : zero mode contribution mock melting of 1P quarkonium states (Umeda , 2006, Mocsy, P.P, 2007), threshold enhancement leads to almost T-independent quarkonium correlators ( Mocsy, P.P, 2007) QWG2008, Nara, December 2-5, 2008

Color screening in QCD and quarkonia melting Confined Deconfined r V(r) T/TC 1/r [fm-1] (1S) J/(1S) c(1P) ’(2S) b’(2P) ’’(3S) Matsui and Satz, 1986 Color screening reduces the effective range of interactions in QGP Other medium effects (e.g. Landau damping) produce an imaginary part for the potential (Laine et al, 2006, Blaizot 2007, Brambilla et al, 2008, Escobeto and Soto, 2008) use quarkonia as thermometer of the matter created in RHIC

Color screening in QCD and quarkonia melting RBC-Bielefeld Collaboration, 2+f lattice QCD

Meson correlators and spectral functions LGT Imaginary time Real time Study the ratio MEM If there is no T-dependence in the spectral function

many gluon exchanges important near threshold Quarkonium spectral functions in potential models  ~ MJ/ , s0 nonrelativistic   s0 perturbative + many gluon exchanges important near threshold S-wave P-wave use lattice data on the quark anti-quark free energy to construct the potential compare to lattice QCD results Mócsy, P.P., PRL 99 (07) 211602, PRD77 (08) 014501, EPJC ST 155 (08) 101

c resonance-like structures disappear already by 1.2Tc strong threshold enhancement above free case indication of correlations height of bump in lattice and model are similar The correlators do not change significantly despite the melting of the bound states

c resonance-like structures disappear already by 1.2Tc strong threshold enhancement above free case indication of correlations height of bump in lattice and model are similar The correlators do not change significantly despite the melting of the bound states

resonance-like structures disappear already by 1.2Tc strong threshold enhancement above free case indication of correlations height of bump in lattice and model are similar The correlators do not change significantly despite the melting of the bound states

Quarkonium binding energy and thermal width Using lattice data on the static quark anti-quark free energy in 2+1f QCD the binding energy of different quarkonium states can be estimated Mócsy, P.P., PRL 99 (07) 211602 Kharzeev, McLerran, Satz, PLB356 (95) 349

Quarkonium binding energy in different models Alberico et al, PRD72 (05) 114011 binding energy decreases with T, but there are large uncertanties from modeling of V

Quarkonium width in different models Park et al, PRC76 (07) 044907 Zhao, Rapp, PLB664 (08) 253 NLO pQCD + in-medium binding energy quasi-free dissociation in-medium binding energy quark gluon Reduced binding energy => larger width; thermal width increases with T above deconfinement

Spectral functions with complex potential Burnier, Laine, Vepsalainen JHEP 0801 (08) 043 The imaginary part of the potential washes out the bound state peak making it a mere threshold enhancement even for b-quarks ! Large threshold enhancement is observed

Summary Lattice and perturbative calculations show that in-medium modification of the potential is sufficiently strong to lead to quarkonium dissociation in the deconfined phase Residual interaction of quark and anti-quark are important  threshold enhancement very small T-dependence of Euclidean correlators conclusions reached in lattice calculations of the Euclidean correlators and spectral functions about the survival of 1S state (Umeda et al, 2002; Asakawa, Hatsuda, 2003, Datta et al, 2003) were premature ! MEM is not sufficiently accurate Potential model calculations based on lattice results on singlet free energy reproduce the temperature (in)dependence of the Euclidean time correlators Crosscheck : threshold enhancement effects weaken with decreasing quark masses  larger T-dependence for quarkonium correlators (consistent with lattice calculations of Datta et al) Lattice calculations based on “wave function method” indicate survival of charmonium states till 2.3Tc (Umeda et al, 2000, 2008) Problems : even highly excited states, e.g. 2P states survive to such high T the notion of well defined states is problematic due to finite width effect Crosscheck : consider the light quark case where no bound states are expected, c.f. lattice calculations of fluctuations of conserved charges.

Outlook Combine EFT techniques in the weak coupling regime with available lattice data on the static meson correlators to obtain a reliable potential model type of framework with all medium effect included. Calculate charm fluctuations to find the relevant degrees of freedom : bound states or free quark. Determine the quasi-particle properties at high T Extend the lattice “wave function analysis” to light quark sector to check the consistency of the approach

Backup slides