Lattice QCD constraints on the heavy quark diffusion coefficient

We report progress towards computing the heavy quark momentum diffusion coefficient from the correlator of two chromo-electric fields attached to a Polyakov loop in pure SU(3) gauge theory. Using a multilevel algorithm and tree-level improvement, we study the behavior of the diffusion coefficient as a function of temperature in the wide range $1.1<T\mathrm{/}{T}_c<{10}^4$ in order to compare it to perturbative expansions at high temperature. We find that within errors the lattice results are remarkably compatible with the next-to-leading order perturbative result.