Abstract
We calculate the shear viscosity (η) and bulk viscosity (ζ) to entropy density (s) ratios η/s and ζ/s of a gluon plasma system in kinetic theory, including both the elastic forward scattering and the inelastic soft gluon bremsstrahlung processes. Due to the suppressed contribution to η and ζ in the forward scattering and the effective gluon splitting, Arnold, Moore and Yaffe (AMY) and Arnold, Dogan and Moore (ADM) have got the leading order computations for η and ζ in high-temperature QCD matter. In this paper, we calculate the correction to η and ζ in the soft gluon bremsstrahlung process with an analytic method. We find that the contribution of the collision term from the soft gluon bremsstrahlung process is just a small perturbation to the scattering process and that the correction is at ∼5% level. Then, we obtain the bulk viscosity of the gluon plasma for the number-changing process. Furthermore, our leading-order result for bulk viscosity is the formula in high-temperature gluon plasma.
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