A way to estimate the heavy quark thermalization rate from the lattice

TL;DR

This paper proposes a new method to estimate the heavy quark thermalization rate from lattice QCD by relating it to a Euclidean correlation function, potentially reducing systematic uncertainties.

Contribution

It introduces a novel Euclidean correlator involving color-electric fields along a Polyakov loop to determine the heavy quark momentum diffusion coefficient.

Findings

Spectral function is relatively flat at small frequencies.

Method may allow more reliable lattice determination of thermalization rate.

Potential reduction in systematic uncertainties compared to other transport coefficients.

Abstract

The thermalization rate of a heavy quark is related to its momentum diffusion coefficient. Starting from a Kubo relation and using the framework of the heavy quark effective theory, we argue that in the large-mass limit the momentum diffusion coefficient can be defined through a certain Euclidean correlation function, involving color-electric fields along a Polyakov loop. Furthermore, carrying out a perturbative computation, we demonstrate that the spectral function corresponding to this correlator is relatively flat at small frequencies. Therefore, unlike in the case of several other transport coefficients, for which the narrowness of the transport peak makes analytic continuation from Euclidean lattice data susceptible to severe systematic uncertainties, it appears that the determination of the heavy quark thermalization rate could be relatively well under control.