Shear and bulk viscosity of high-temperature gluon plasma

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 gg?gg forward scattering and the inelastic soft gluon bremsstrahlung gg?ggg processes. Due to the suppressed contribution to η and ζ in the gg?gg forward scattering and the effective g?gg 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 gg?ggg process with an analytic method.We find that the contribution of the collision term from the gg?ggg soft gluon bremsstrahlung process is just a small perturbation to the gg?gg 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 ζ∝(αs~2 T~3)/(lnαs-1) in high-temperature gluon plasma.