Heavy quark diffusion in QCD and N=4 SYM at next-to-leading order

TL;DR

This paper calculates the next-to-leading order momentum diffusion coefficient for heavy quarks in hot QCD and N=4 SYM plasmas, revealing the importance of interference effects and soft gauge field physics.

Contribution

It provides the first detailed NLO calculation of heavy quark diffusion in both QCD and N=4 SYM, including new correction terms and extending previous leading-order results.

Findings

NLO correction includes interference and soft gauge effects

Explicit formulas for diffusion constants in QCD and SYM

Poor convergence of perturbation theory without resummation

Abstract

We present the full details of a calculation at next-to-leading order of the momentum diffusion coefficient of a heavy quark in a hot, weakly coupled, QCD plasma. Corrections arise at O(g_s); physically they represent interference between overlapping scatterings, as well as soft, electric scale (p ~ 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 = (16\pi/3) alpha_s^2 T^3 (log(1/g) + 0.07428 + 1.9026 g). We extend the computation to a heavy fundamental representation ``probe'' quark in large N_c, N=4 Super Yang-Mills theory, where the result is kappa^{SYM}= (lambda^2 T^3)(6\pi) (log(1/\sqrt{\lambda}) + 0.4304 + 0.8010 \sqrt{lambda}) (where lambda=g_s^2 N_c is the t'Hooft coupling). In the absence of some resummation technique, the convergence of perturbation theory is poor.