Quarkonia and heavy-quark relaxation times in the quark-gluon plasma

Abstract

A thermodynamic T-matrix approach for elastic 2-body interactions is employed to calculate spectral functions of open and hidden heavy-quark systems in the Quark-Gluon Plasma. This enables the evaluation of quarkonium bound-state properties and heavy-quark diffusion on a common basis and thus to obtain mutual constraints. The two-body interaction kernel is approximated within a potential picture for spacelike momentum transfers. An effective field-theoretical model combining color-Coulomb and confining terms is implemented with relativistic corrections and for different color channels. Four pertinent model parameters, characterizing the coupling strengths and screening, are adjusted to reproduce the color-average heavy-quark free energy as computed in thermal lattice QCD. The approach is tested against vacuum spectroscopy in the open (D, B) and hidden (Psi and Upsilon) flavor sectors, as well as in the high-energy limit of elastic perturbative QCD scattering. Theoretical uncertainties in the static reduction scheme of the 4-dimensional Bethe-Salpeter equation are elucidated. The quarkonium spectral functions are used to calculate Euclidean correlators which are discussed in light of lattice QCD results, while heavy-quark relaxation rates and diffusion coefficients are extracted utilizing a Fokker-Planck equation.