The shear viscosity of quark-gluon matter calculated with parton transport and comparisons with the Chapman-Enskog results

We numerically calculate the shear viscosity of quark-gluon matter via the Green-Kubo relation with an improved ZPC model. We include all $2\leftrightarrow 2$ parton cross sections at finite temperature, which are based on perturbative QCD and screened with thermal masses, and consider massless quark-gluon systems with Boltzmann statistics in chemical equilibrium. We then compare the Green-Kubo results with the analytical results from the leading-order Chapman-Enskog method for the same parton cross sections over the temperature range $150-600$ MeV. We also examine the simpler case of isotropic and constant parton cross sections. Overall, we find that the two methods agree rather well. Specifically, the Green-Kubo results are greater than the Chapman-Enskog results by an average of $\sim 9\mathrm{\%}$ for isotropic and constant cross sections and by an average of $\sim 3\mathrm{\%}$ for finite-temperature pQCD cross sections, where the difference between the two methods is presumably due to higher-order corrections to the leading-order Chapman-Enskog results.