1-loop matching of a thermal Lorentz force

M Laine

doi:10.1007/jhep06(2021)139

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 left(sqrt{MT},Tright) , 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.

Highlights

∼ M/(α2T 2) [6]
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
For M T, there should be a broad range of time scales for which eq (1.1) is valid

Summary

Outline of a procedure

(2.1) and (2.2) are subject to wave function renormalization, which drops out in the ratio aQi CD It is for the cause of such an acceleration, multiplied by a (thermally corrected) pole mass M , that we would like to find an operator reminiscent of the Lorentz force. We take a trace in Dirac space, given that the operator we are interested in, cf eq (2.5), is spinindependent The part of this correlator proportional to e−βM originates from the single heavy quark sector of the Hilbert space, and gives the effects that we are interested in. One can envisage a more radical reduction, to which we refer as an infrared (IR) description This involves an operator reminiscent of the Lorentz force in eq (1.1), FiIR ≡ − igB θ† ZE Fi0V0 + ZB Fij Vj θ ,. This establishes the principal viability of a dynamics like that in eq (1.1). Such dynamics has already been employed for deriving purely gluonic 2-point imaginary-time correlators, permitting to study features of heavy quark diffusion and kinetic equilibration [3,4,5]

QCD vacuum contribution

QCD thermal contribution

Non-relativistic determination of the thermal contribution

Infrared side of the matching

Result and discussion