Re-running the QCD shear viscosity

TL;DR

This paper re-examines the shear viscosity to entropy density ratio of the quark-gluon plasma using an improved perturbative QCD approach, suggesting that low viscosity values can be explained perturbatively rather than non-perturbatively.

Contribution

It introduces a kinetic scheme with running coupling and thermal screening considerations to better estimate QGP shear viscosity within perturbative QCD.

Findings

Estimated η/s ≈ 0.2 within perturbative QCD

Higher-order corrections reduce the need for non-perturbative explanations

Resummation improves the perturbative estimate of QGP viscosity

Abstract

The remarkably small shear viscosity to entropy density ratio $\eta/s < 0.5$ of the quark-gluon plasma (QGP) is a key insight from heavy ion experiments. Nonetheless, the basic understanding of this `observable' still seems to be rudimentary, with existing perturbative QCD estimates suggesting $\eta/s > 1$, a view that we scrutinize here. In order to extrapolate the available perturbative approach to phenomenologically relevant temperatures, we consider carefully controllable higher-order corrections: We adapt the leading-order effective kinetic scheme (instead of the catchy next-to-leading log formula $\eta_{_{{\rm NLL}}} \propto [\alpha^2 \log(c/\alpha)]^{-1}$), by using cross sections with a running coupling. This effect should be pertinent (for a QGP) and we argue for a choice of scale-dependence that makes it consistent with thermal screening. We conclude that $\eta/s \approx 0.2$ does not indicate genuine non-perturbative effects, it may rather be understood within resummation-improved perturbative QCD, with some uncertainties from deploying kinetic theory near to its limit.