Thermal imaginary part of a real-time static potential from classical lattice gauge theory simulations

TL;DR

This paper demonstrates how classical lattice gauge theory simulations can non-perturbatively measure the imaginary part of the real-time static potential at finite temperature, confirming its existence and semi-quantitative agreement with perturbative predictions.

Contribution

It introduces a method to measure the imaginary part of the static potential non-perturbatively using classical lattice simulations, linking it to Landau damping effects.

Findings

Non-perturbative imaginary part exists.

Measured imaginary part agrees semi-quantitatively with perturbation theory.

Method accounts for infrared sector of finite-temperature field theory.

Abstract

Recently, a finite-temperature real-time static potential has been introduced via a Schr\"odinger-type equation satisfied by a certain heavy quarkonium Green's function. Furthermore, it has been pointed out that it possesses an imaginary part, which induces a finite width for the tip of the quarkonium peak in the thermal dilepton production rate. The imaginary part originates from Landau-damping of low-frequency gauge fields, which are essentially classical due to their high occupation number. Here we show how the imaginary part can be measured with classical lattice gauge theory simulations, accounting non-perturbatively for the infrared sector of finite-temperature field theory. We demonstrate that a non-vanishing imaginary part indeed exists non-perturbatively; and that its value agrees semi-quantitatively with that predicted by Hard Loop resummed perturbation theory.