Shear and bulk viscosities of a gluon plasma in perturbative QCD: Comparison of different treatments for the gg↔ggg process

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 ,w e find that the minimum angle θ among the final-state gluons in the fluid local rest frame has a distribution that is peaked at θ ∼ √ αs, analogous to the near-collinear splitting asserted by AMY and ADM. However, the average of θ is much bigger than its peak value, as its distribution is skewed with a long tail. The same θ behavior 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(Nc) pure gauge theory and summarize the current viscosity computations in QCD.