Transport coefficients from in medium quarkonium dynamics

Abstract

The in medium dynamics of heavy particles are governed by transport coefficients. The heavy quark momentum diffusion coefficient, $κ$, is an object of special interest in the literature, but one which has proven notoriously difficult to estimate, despite the fact that it has been computed by weak-coupling methods at next-to-leading order accuracy, and by lattice simulations of the pure SU(3) gauge theory. Another coefficient, $γ$, has been recently identified. It can be understood as the dispersive counterpart of $κ$. Little is known about $γ$. Both $κ$ and $γ$ are, however, of foremost importance in heavy quarkonium physics as they entirely determine the in and out of equilibrium dynamics of quarkonium in a medium, if the evolution of the density matrix is Markovian, and the motion, quantum Brownian; the medium could be a strongly or weakly coupled plasma. In this paper, using the relation between $κ$, $γ$ and the quarkonium in medium width and mass shift respectively, we evaluate the two coefficients from existing 2+1 flavor lattice QCD data. The resulting range for $κ$ is consistent with earlier determinations, the one for $γ$ is the first non-perturbative determination of this quantity.