Perturbative renormalization of the electric field correlator

TL;DR

This paper calculates the perturbative renormalization factor for a lattice discretization of the electric field correlator in hot QCD, which is crucial for accurately determining the heavy quark momentum diffusion coefficient.

Contribution

It provides the first NLO perturbative renormalization factor for the electric field correlator in Wilson's SU(3) gauge theory, aiding precise lattice QCD calculations.

Findings

Found a ~12% NLO correction for the renormalization factor.

Discussed implications for existing lattice results.

Suggested non-perturbative renormalization via gradient flow.

Abstract

The momentum diffusion coefficient of a heavy quark in a hot QCD plasma can be extracted as a transport coefficient related to the correlator of two colour-electric fields dressing a Polyakov loop. We determine the perturbative renormalization factor for a particular lattice discretization of this correlator within Wilson's SU(3) gauge theory, finding a ~12% NLO correction for values of the bare coupling used in the current generation of simulations. The impact of this result on existing lattice determinations is commented upon, and a possibility for non-perturbative renormalization through the gradient flow is pointed out.