QCD Shear Viscosity at (almost) NLO

TL;DR

This paper calculates the shear viscosity of QCD including nearly all next-to-leading order corrections, revealing large corrections that significantly reduce the viscosity-to-entropy ratio and highlighting issues with the perturbative expansion at high temperatures.

Contribution

It provides a comprehensive NLO calculation of QCD shear viscosity, including almost all corrections suppressed by one power of the coupling, and analyzes their impact on transport properties.

Findings

NLO corrections significantly reduce η/s by over a factor of 3.

The largest correction comes from modifications to the qhat parameter.

Perturbative expansion remains problematic at temperatures around 100 GeV.

Abstract

We compute the shear viscosity of QCD with matter, including almost all next-to-leading order corrections -- that is, corrections suppressed by one power of $g$ relative to leading order. We argue that the still missing terms are small. The next-to-leading order corrections are large and bring $\eta/s$ down by more than a factor of 3 at physically relevant couplings. The perturbative expansion is problematic even at $T \simeq 100$ GeV. The largest next-to-leading order correction to $\eta/s$ arises from modifications to the qhat parameter, which determines the rate of transverse momentum diffusion. We also explore quark number diffusion, and shear viscosity in pure-glue QCD and in QED.