Heavy Quarkonia in Quark-Gluon Plasma

Does the $Q$-$\bar Q$ potential from lattice gauge data yield a $J/\psi$ dissociation temperature $\sim $1.6 $T_c$ as in lattice spectral function analyses? Is there a strong coupling between a static $Q$ and $\bar Q$ in their color-singlet states in the quark-gluon plasma? From a variational principle, we find the color-singlet $Q$-$\bar Q$ potential to be $f_F F_1+(1-f_F) U_1$, where $F_1$ is the lattice gauge color-singlet free energy, $U_1$ the internal energy, $f_F=3/(3+a(T))$, and $a(T)=$3(pressure)/(energy density) is from the equation of state. We find that $J/\psi$ dissociates spontaneously above 1.56 $T_c$, while $\chi_c$ and $\psi'$ are unbound in the quark-gluon plasma. Our analysis lends support to the theoretical result that $J/\psi$ is bound up to $\sim$1.6 $T_c$. However, $J/\psi$ has a binding energy $\sim$ 0.04 GeV at 1.13 $T_c$, indicating that the coupling between a static $Q$ and $\bar Q$ in their color-singlet states is quite weak in the quark-gluon plasma. For details, please browse http://www.arxiv.org/pdf/hep-ph/0408020.