The imaginary part of the heavy-quark potential from real-time Yang-Mills dynamics

We extract the imaginary part of the heavy-quark potential using classical-statistical simulations of real-time Yang-Mills dynamics in classical thermal equilibrium. The $r$-dependence of the imaginary part of the potential is extracted by measuring the temporal decay of Wilson loops of spatial length $r$. We compare our results to continuum expressions obtained using hard thermal loop theory and to semi-analytic lattice perturbation theory calculations using the hard classical loop formalism. We find that, when plotted as a function of $m_D r$, where $m_D$ is the hard classical loop Debye mass, the imaginary part of the heavy-quark potential is independent of the lattice spacing at small $r$ and agrees well with the semi-analytic hard classical loop result. For large quark-antiquark separations, we quantify the magnitude of the non-perturbative long-range corrections to the imaginary part of the heavy-quark potential. We present our results for a wide range of temperatures, lattice spacings, and lattice volumes. Based on our results, we extract an estimate of the heavy-quark transport coefficient $\kappa$ from the short-distance behavior of the classical potential and compare our result with $\kappa$ obtained using hard thermal loops and hard classical loops. This work sets the stage for extracting the imaginary part of the heavy-quark potential in an expanding non-equilibrium Yang Mills plasma.