We study the evolution of heavy quarkonium states with temperature in a quark-gluon plasma (QGP) by evaluating the in-medium $Q\mathrm{\text{−}}\overline{Q}$ $T$-matrix within a reduced Bethe-Salpeter equation in both $S$- and $P$-wave channels. The underlying interaction kernel is extracted from recent finite-temperature QCD lattice calculations of the singlet free energy of a $Q\mathrm{\text{−}}\overline{Q}$ pair. The bound states are found to gradually move above the $Q\mathrm{\text{−}}\overline{Q}$ threshold after which they rapidly dissolve in the hot system. The $T$-matrix approach is particularly suited to investigate these mechanisms as it provides a unified treatment of bound and scattering states including threshold effects and the transition to the (perturbative) continuum. We apply the $T$-matrix to calculate $Q\mathrm{\text{−}}\overline{Q}$ spectral functions as well as pertinent Euclidean-time correlation functions which are compared to results from lattice QCD. A detailed analysis reveals large sensitivities to the interplay of bound and scattering states, to temperature-dependent threshold energies, and to the reconstructed correlator used for normalization. We furthermore investigate the impact of finite-width effects on the single-quark propagators in the QGP as estimated from recent applications of heavy-quark rescattering to RHIC data.

• Received 17 November 2006

DOI:https://doi.org/10.1103/PhysRevD.76.114506