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

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.