Jiunn-Wei Chen, Jian Deng, Hui Dong, Qun Wang
The leading order contribution to the shear and bulk viscosities, $\eta $ and $\zeta $, of a gluon plasma in perturbative QCD includes the $gg\leftrightarrow gg$ (22) process, $gg\leftrightarrow ggg$ (23) process and multiple scattering processes known as the Landau-Pomeranchuk-Migdal (LPM) effect. Complete leading order computations for $\eta $ and $\zeta $ were obtained by Arnold, Moore and Yaffe (AMY) and Arnold, Dogan and Moore (ADM), respectively, with the inelastic processes computed by an effective $g\leftrightarrow gg$ 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 we agree with their results within errors. By studying the 23 contribution to $\eta $, we find that the minimum angle among the final state gluons $\theta $ in the fluid local rest frame has a distribution that is peaked at $\theta \sim \sqrt{\alpha_{s}}$, analogous to the near collinear splitting asserted by AMY and ADM. However, the average of $\theta $ is much bigger than its peak value, as its distribution is skewed with a long tail. The same $\theta $ 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 $SU(N_{c})$ pure gauge theory and summarize the current viscosity computations in QCD.
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http://arxiv.org/abs/1107.0522
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