Heavy Quark Thermalization in Classical Lattice Gauge Theory: Lessons for Strongly-Coupled QCD

TL;DR

This paper investigates heavy quark thermalization in classical lattice gauge theory, revealing that weak-coupling approximations underestimate the rate and providing insights into the spectral function shape relevant for lattice QCD studies.

Contribution

It demonstrates non-perturbative effects on heavy quark thermalization rates and explores the spectral function shape, bridging classical simulations with hot QCD dynamics.

Findings

Weak-coupling expansion underestimates thermalization rate

Classical lattice simulations reveal significant non-perturbative effects

Spectral function shape insights aid Euclidean lattice reconstructions

Abstract

Thermalization of a heavy quark near rest is controlled by the correlator of two electric fields along a temporal Wilson line. We address this correlator within real-time, classical lattice Yang-Mills theory, and elaborate on the analogies that exist with the dynamics of hot QCD. In the weak-coupling limit, it can be shown analytically that the dynamics on the two sides are closely related to each other. For intermediate couplings, we carry out non-perturbative simulations within the classical theory, showing that the leading term in the weak-coupling expansion significantly underestimates the heavy quark thermalization rate. Our analytic and numerical results also yield a general understanding concerning the overall shape of the spectral function corresponding to the electric field correlator, which may be helpful in subsequent efforts to reconstruct it from Euclidean lattice Monte Carlo simulations.