Paper detail

Shear and Bulk Viscosities of a Gluon Plasma in Perturbative QCD: Comparison of Different Treatments for the gg<->ggg Process

The leading order contribution to the shear and bulk viscosities, ηand ζ, of a gluon plasma in perturbative QCD includes the gg -> gg (22) process, gg <-> ggg (23) process and multiple scattering processes known as the Landau-Pomeranchuk-Migdal (LPM) effect. Complete leading order computations for ηand ζwere obtained by Arnold, Moore and Yaffe (AMY) and Arnold, Dogan and Moore (ADM), respectively, with the inelastic processes computed by an effective g <-> gg gluon splitting. We study how complementary calculations with 22 and 23 processes and a simple treatment to model the LPM effect compare with the results of AMY and ADM. We find that our results agree with theirs within errors. By studying the contribution of the 23 process to η, we find that the minimum angle θamong the final state gluons in the fluid local rest frame has a distribution that is peaked at θ\sim \sqrt{α_{s}}, analogous to the near collinear splitting asserted by AMY and ADM. However, the average of θis much bigger than its peak value, as its distribution is skewed with a long tail. The same θbehavior is also seen if the 23 matrix element is taken to the soft gluon bremsstrahlung limit in the center-of-mass (CM) frame. This suggests that the soft gluon bremsstrahlung in the CM frame still has some near collinear behavior in the fluid local rest frame. We also generalize our result to a general SU(N_c) pure gauge theory and summarize the current viscosity computations in QCD.