Thermal Modification of Quarkonium Spectral Functions from QCD Sum Rules with the Maximum Entropy Method

The quarkonium spectral functions at finite temperature are analyzed by employing QCD sum rules with the maximum entropy method. This approach enables us to extract the spectral functions without any phenomenological parametrization, and thus to visualize deformation of the spectral functions due to temperature effects driven by change of gluon condensates, which can be estimated in lattice QCD. As a result, it is found that the charmonium ground states of both S-wave and P-wave channels disappear at temperatures around or slightly above the critical temperatureTc, while the bottomonium states survive up to well above Tc, at least 2.5Tc for S-wave states and around 2 .0Tc for P-wave states. Furthermore, a detailed analysis of Υ state shows that the obtained lowest peak at T=0 contains contribution not only from the ground state but also from the excited states, Υ(2S) andΥ(3S). Our results at finiteT are consistent with the picture that the excited states of bottomonia dissociate at lower temperature than that of the ground state. Assuming this picture, we find that Υ(2S) andΥ(3S) disappear at T = 1.5−2.0Tc.