Abstract
Using the color-singlet free energy and total internal energy obtained by Kaczmarek et al. (hep-lat/0309121) for a static quark Q and an antiquark 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 potential can be obtained from the total internal energy 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 potential is approximately for and it changes to at high temperatures. In this potential model, the is weakly bound above the phase-transition temperature , and it dissociates spontaneously above , whereas and are unbound in the quark-gluon plasma. The bottomium states , and are bound in the quark-gluon plasma and they dissociate at and respectively. For comparison, we evaluate the heavy quarkonium binding energies also in other models using the free energy or the total internal energy as the potential. The comparison shows that the model with the new potential proposed here gives dissociation temperatures that agree best with those from spectral function analyses. We evaluate the cross section for and its inverse process to determine the dissociation width and the rate of production by recombining c and in the quark-gluon plasma.
9 More- Received 2 August 2004
DOI:https://doi.org/10.1103/PhysRevC.72.034906
©2005 American Physical Society