Shear viscosity of a massless quark-gluon gas in chemical equilibrium including all $2\leftrightarrow 2$ cross sections

TL;DR

This paper derives an analytical expression for the shear viscosity of a massless quark-gluon gas in chemical equilibrium, including all elastic and inelastic $2 ightarrow 2$ scatterings, aiding the understanding of quark-gluon plasma properties.

Contribution

It provides the first analytical derivation of shear viscosity for a massless quark-gluon gas with all $2 ightarrow 2$ scatterings, including inelastic processes, using the Chapman-Enskog method.

Findings

Derived explicit analytical formulas for shear viscosity with all relevant cross sections.

Verified the single-species limit matches known results.

Presented analytical relations useful for parton transport models.

Abstract

The analytical expressions of the shear viscosity of both one and two particle species with Boltzmann statistics and $2 \rightarrow 2$ elastic scatterings are known from the Chapman-Enskog method and have been shown to be quite accurate. The expression for a multi-species hadronic gas under $2 \rightarrow 2$ elastic scatterings is also known. Here we use the Chapman-Enskog method to derive the shear viscosity of a massless quark-gluon gas of $N_f$ quark flavors in chemical equilibrium subjected to all $2 \rightarrow 2$ parton scatterings including for the first time inelastic scatterings. We then verify the relation in a general single-species limit, where the shear viscosity of the quark-gluon gas should reduce to the result for a single particle species. In addition, we show the explicit analytical result in terms of the seven independent cross sections for the special case of isotropic and energy-independent cross sections. The analytical relations derived here can be useful for determining the shear viscosity of parton transport models with any $2 \rightarrow 2$ scattering cross sections. They can also be coupled with finite temperature QCD cross sections to help study the shear viscosity of the quark gluon plasma.