1-loop matching of a thermal Lorentz force

TL;DR

This paper derives 1-loop matching coefficients for the electric and magnetic components of a Lorentz force acting on heavy quarks in a hot QCD medium, facilitating better understanding of their diffusion and equilibration.

Contribution

It provides the first detailed calculation of 1-loop matching coefficients for the Lorentz force in a thermal QCD setting, including the magnetic part with a non-zero anomalous dimension.

Findings

Magnetic part has a non-zero anomalous dimension.

Matching coefficients enable lattice studies of colour-magnetic correlators.

Results agree with previous thermal and vacuum analyses.

Abstract

Studying the diffusion and kinetic equilibration of heavy quarks within a hot QCD medium profits from the knowledge of a coloured Lorentz force that acts on them. Starting from the spatial components of the vector current, and carrying out two matching computations, one for the heavy quark mass scale ($M$) and another for thermal scales ($\sqrt{MT}$, $T$), we determine 1-loop matching coefficients for the electric and magnetic parts of a Lorentz force. The magnetic part has a non-zero anomalous dimension, which agrees with that extracted from two other considerations, one thermal and the other in vacuum. The matching coefficient could enable a lattice study of a colour-magnetic 2-point correlator.