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

TL;DR

This study uses classical-statistical simulations of real-time Yang-Mills dynamics to extract the imaginary part of the heavy-quark potential, comparing results with theoretical models and exploring non-perturbative effects across various conditions.

Contribution

It provides a novel non-perturbative calculation of the imaginary part of the heavy-quark potential from real-time Yang-Mills simulations, including its dependence on separation and temperature.

Findings

Good agreement with semi-analytic hard classical loop results at small distances.

Identification of non-perturbative long-range corrections at large separations.

Minimal lattice spacing sensitivity for small $m_D r$ values.

Abstract

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 shows little sensitivity to the lattice spacing at small $m_D r \lesssim 1$ 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. This work sets the stage for extracting the imaginary part of the heavy-quark potential in an expanding non-equilibrium Yang Mills plasma.