Heavy quarkonia in quark-gluon plasma

Using the color-singlet free energy $F_1$ and total internal energy $U_1$ obtained by Kaczmarek et al. (hep-lat/0309121) for a static quark Q and an antiquark $\overline{Q}$ 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 $Q\text{−}\overline{Q}$ 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 $Q\text{−}\overline{Q}$ potential is approximately $F_1$ for $T~T_c$ and it changes to $\frac{3}{4}{F}_1+\frac{1}{4}{U}_1$ 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 ${\psi }^{\text{'}}$ are unbound in the quark-gluon plasma. The bottomium states $\Upsilon ,{\chi }_b$, and ${\Upsilon }^{\text{'}}$ 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 $Q\text{−}\overline{Q}$ potential. The comparison shows that the model with the new $Q\text{−}\overline{Q}$ potential proposed here gives dissociation temperatures that agree best with those from spectral function analyses. We evaluate the cross section for $\sigma (g+J/\psi \to c+\overline{c})$ and its inverse process to determine the $J/\psi$ dissociation width and the rate of $J/\psi$ production by recombining c and $\overline{c}$ in the quark-gluon plasma.