Heavy quarkonia in quark-gluon plasma

Using the color-singlet free energy F₁ and total internal energy U₁ obtained by Kaczmarek et al. (hep-lat/0309121) for a static quark Q and an antiquark Q̄ 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-Q̄ potential can be obtained from the total internal energy U₁ 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-Q̄ potential is approximately F₁ for T~Tc and it changes to 3/4F₁+1/4U₁ at high temperatures. In this potential model, the J/ψ is weakly bound above the phase-transition temperature Tc, and it dissociates spontaneously above 1.62Tc, whereas χc and ψ' are unbound in the quark-gluon plasma. The bottomium states Υ,χb, and Υ' are bound in the quark-gluon plasma and they dissociate at 4.1Tc,1.18Tc, and 1.38Tc respectively. For comparison, we evaluate the heavy quarkonium binding energies also in other models using the free energy F₁ or the total internal energy U₁ as the Q-Q̄ potential. The comparison shows that the model with the new Q-Q̄ potential proposed here gives dissociation temperatures that agree best with those from spectral function analyses. We evaluate the cross section for σ(g+J/ψ→c+c̄) and its inverse process to determine the J/ψ dissociation width and the rate of J/ψ production by recombining c and c̄ in the quark-gluon plasma.