We extract the $Q\text{−}\overline{Q}$ potential by using the thermodynamic quantities obtained in lattice gauge calculations. The potential is tested and found to give spontaneous dissociation temperatures that agree well with those from lattice gauge spectral function analysis. Using such a $Q\text{−}\overline{Q}$ potential, we examine the quarkonium states in a quark-gluon plasma and determine the “quark drip lines” which separate the region of bound color-singlet $Q\overline{Q}$ states from the unbound region. The characteristics of the quark drip lines severely limit the region of possible bound $Q\overline{Q}$ states with light quarks to temperatures close to the phase transition temperature. Bound quarkonia with light quarks may exist very near the phase transition temperature if their effective quark mass is of the order of 300–400 MeV and higher.

• Received 19 June 2006

DOI:https://doi.org/10.1103/PhysRevC.76.014902