The shear viscosity of a gluon gas is calculated using the Green-Kubo relation. Time correlations of the energy-momentum tensor in thermal equilibrium are extracted from microscopic simulations using a parton cascade solving various Boltzmann collision processes. We find that the perturbation-QCD- (pQCD-) based gluon bremsstrahlung described by Gunion-Bertsch processes significantly lowers the shear viscosity by a factor of 3 to 8 compared to elastic scatterings. The shear viscosity scales with the coupling as $\eta \sim 1/\left[{\alpha }_s^2\log (1/{\alpha }_s)\right]$. For constant ${\alpha }_s$ the shear viscosity to entropy density ratio $\eta /s$ has no dependence on temperature. Replacing the pQCD-based collision angle distribution of binary scatterings by an isotropic form decreases the shear viscosity by a factor of 3.

• Received 20 July 2011

DOI:https://doi.org/10.1103/PhysRevC.84.054911