Heavy Quarkonia in Quark-Gluon Plasma

Using the color-singlet quark-antiquark potential obtained by Kaczmarek $et al.$ from quenched lattice QCD theory, we study the binding energies and wave functions of heavy quarkonia in quark-gluon plasma above the transition temperature $T_c$. We find that $J/\psi$ dissociates spontaneously at $\sim 2 T_c$, $\chi_c$ and $\psi'$ at $\sim 1.2 T_c$, $\Upsilon$ at $\sim 4.5 T_c$, and $\chi_b$ and $ \Upsilon'$ at $\sim 2 T_c$. A comparison of the dissociation temperatures in this potential model analysis and the spectral function analyses of Asakawa $et al.$ and Petreczky $et al.$ indicates qualitative agreement that $J/\psi$ and $\chi$ are stable at a temperature slightly above $T_c$ and dissociate spontaneously at higher temperatures. It is, however, not necessary to reach the temperature for spontaneous dissociation with zero binding energy for a quarkonium to dissociate. A quarkonium can dissociate by thermalization and by collision with gluons in quark-gluon plasma. We evaluate the cross section for $J/\psi$ dissociation in collision with gluons, $\sigma(g+ J/\psi \to c + \bar c)$, and calculate the $J/\psi$ collisional dissociation rate and collisional dissociation width. The $J/\psi$ binding energy is equal to its collisional dissociation width at $\sim 1.2 T_c$, indicating a strong instability for $J/\psi$ collisional dissociation if the temperature greatly exceeds 1.2 $T_c$. To study the production of $J/\psi$ by the recombination of charm quarks and antiquarks, we calculate the cross section for the reaction $c + \bar c \to g+ J/\psi$ and determine the rate of $J/\psi$ production arising from the collision of charm quarks and antiquarks in quark gluon plasma.