Continuum Study of Heavy Quark Diffusion

We report on a lattice investigation of heavy quark momentum diffusion within the pure SU(3) plasma above the deconfinement transition with the quarks treated to leading order in the heavy mass expansion. We measure the relevant “colour-electric” Euclidean correlator and based on several lattice spacing’s perform the continuum extrapolation. This is necessary not only to remove cut-off effects but also the analytic continuation for the extraction of transport coefficients is well-defined only when a continuous function of the Euclidean time variable is available. We pay specific attention to scale setting in SU(3). In particular we present our determination for the critical temperature $T_c=1\mathrm{/}(N_{\tau }a)$ at values of $N_{\tau }\le 22$.