Heavy quark diffusion in perturbative QCD at next-to-leading order

TL;DR

This paper calculates the next-to-leading order correction to the momentum diffusion coefficient of a heavy quark in a hot QCD plasma, revealing the complexity and poor convergence of the weak coupling expansion.

Contribution

It provides the first NLO calculation of heavy quark momentum diffusion in QCD, incorporating interference effects and soft gauge field physics using HTL theory.

Findings

NLO correction includes interference and soft gauge effects

The diffusion constant formula involves a logarithmic and linear term in g

Weak coupling expansion shows poor convergence

Abstract

We compute the momentum diffusion coefficient of a nonrelativistic heavy quark in a hot QCD plasma, to next-to-leading order in the weak coupling expansion. Corrections arise at O(g); physically they represent interference between overlapping scatterings, as well as soft, electric scale ($p\sim gT$) gauge field physics, which we treat using the hard thermal loop (HTL) effective theory. In 3-color, 3-flavor QCD, the momentum diffusion constant of a fundamental representation heavy quark at NLO is $\kappa = \frac{16\pi}{3} \alpha_s^2 T^3 (\ln \frac{1}{g} + 0.07428 + 1.8869 g)$. The convergence of the weak coupling expansion is poor.