Heavy quarkonia in quark-gluon plasma

Using the color-singlet free energy F-1 and total internal energy U-1 obtained by Kaczmarek (hep-lat/0309121) for a static quark Q and an antiquark (Q) over bar in quenched QCD, we study the binding energies and wave functions of heavy quarkonia in a quark-gluon plasma. By minimizing the grand potential in a simplified schematic model, we find that the proper color-singlet Q-(Q) over bar potential can be obtained from the total internal energy U-1 by subtracting the gluon internal energy contributions. We carry out this subtraction in the local energy-density approximation in which the gluon energy density can be related to the local gluon pressure by the quark-gluon plasma equation of state. We find in this approximation that the proper color-singlet Q-(Q) over bar potential is approximately F-1 for T similar to T-c and it changes to 3/4F(1) + 1/4U(1) at high temperatures. In this potential model, the J/psi is weakly bound above the phase-transition temperature T-c, and it dissociates spontaneously above 1.62T(c), whereas chi(c) and psi(') are unbound in the quark-gluon plasma. The bottomium states Upsilon,chi(b), and Upsilon(') are bound in the quark-gluon plasma and they dissociate at 4.1T(c),1.18T(c), and 1.38T(c) respectively. For comparison, we evaluate the heavy quarkonium binding energies also in other models using the free energy F-1 or the total internal energy U-1 as the Q-(Q) over bar potential. The comparison shows that the model with the new Q-(Q) over bar potential proposed here gives dissociation temperatures that agree best with those from spectral function analyses. We evaluate the cross section for sigma(g+J/psi -> c+(c) over bar) and its inverse process to determine the J/psi dissociation width and the rate of J/psi production by recombining c and (c) over bar in the quark-gluon plasma.