Re-running the QCD shear viscosity

The remarkably small shear viscosity to entropy density ratio $\eta /s\lesssim 0.5$ 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 $\eta /s\gtrsim 1$—a view that we scrutinise 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 ${\eta }_{{}_{NLL}}\propto {\left[{\alpha }^{2}log\right(c/\alpha \left)\right]}^{-1}$), 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 $\eta /s\lesssim 0.5$ 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. (paper)