Viscosities Of High-temperature QCD In The Effective Kinetic Theory

Viscosities which characterize the transport properties of a system evolving from non-equilibrium to equilibrium states have been attracted wide and intense inter-ests.However, to calculate viscosities whether in non-equilibrium statistical physics or in hydrodynamics, is a very complicated task. Viscosities can be obtained from the Boltzmann equation of effective kinetic theory. But the Boltzmann equation is a differential integral equation,it is very hard to be solved analytically. People can only use some feasible approximation methods to solve this equation. It is generally believed that the hot dense QCD matter is likely to be weakly interacted when the temperature and/or density is asymptotically high, for instance T,μ>>ΛQCD. The Weakly coupling QCD matter hopefully exists in the early universe or compacting stars. Therefor, it is helpful for us to analyze the structure and evolution of compact stars and the early universe through the viscosities.In this paper,we use the variational method to solve the Boltzmann equations of ef-fective kinetic theory of QCD, and thus obtain the viscosities of weakly coupling QCD matter.The first part mainly introduces the kinetic theory of QCD matter,as theoret-ical basis to calculate its viscousitis.In the second part, we approximately calculate the collision terms of the Boltzmann equation. The third part uses variational method to calculate viscosities of high temperature QCD matter:Firstly, we only include the 2(?)2 scattering process to get the leading order contribution of the shear viscosity of the high-temperature QCD matter. Then by including the contribution of the gg(?)ggg soft gluon bremsstrahlung process in a gluon plasma system, we find that the contribution of the collision term from the gg(?)ggg soft gluon bremsstrahlung process is 4.6 times of that from the 2(?)2 scattering process. Since the collision term contribution decreases the viscosities, we findη22+23/η22(?)17.9%. Finally, we obtain the bulk viscosity of the gluon plasma for a conformal non-invariance system. Furthermore,our result of the viscosity is just 1/10 of that by AMY(Arnold,Moore and Yaffe). The reason is that:they consider the contribution of 1(?)2 splitting process for the particle number violation, while we consider the gg(?)ggg soft gluon bremsstrahlung process for that. This demonstrates that the contribution to the bulk viscosity of the gg(?)ggg soft gluon bremsstrahlung process is more important than that of the 1(?)2 splitting process.