How perfect can a gluon plasma be in perturbative QCD?

The shear viscosity to entropy density ratio, \eta /s, characterizes howperfect a fluid is. We calculate the leading order \eta /s of a gluon plasma inperturbation using the kinetic theory. The leading order contribution onlyinvolves the elastic gg -> gg (22) process and the inelastic gg<->ggg (23)process. The Hard-Thermal-Loop (HTL) treatment is used for the 22 matrixelement, while the exact matrix element in vacuum is supplemented by the gluonDebye mass insertion for the 23 process. Also, the asymptotic mass is used forthe external gluons in the kinetic theory. The errors from not implementing HTLand the Landau-Pomeranchuk-Migdal effect in the 23 process, and from theuncalculated higher order corrections, are estimated. Our result for \eta /slies between that of Arnold, Moore and Yaffe (AMY) and Xu and Greiner (XG). Ourresult shows that although the finite angle contributions are important atintermediate \alpha_s (\alpha_s \sim 0.01-0.1), the 22 process is still moreimportant than 23 when \alpha_s < 0.1. This is in qualitative agreement withAMY's result. We find no indication that the proposed perfect fluid limit \eta/s \simeq 1/(4\pi) can be achieved by perturbative QCD alone.Comment: ReVTex 4, 11 pages, 5 figures. A coding error in the exact matrix element for the 23 process is corrected. Results in Fig. 2,3 and Table I are re-calculated, and relevant discussions are adjusted. Part of the conclusion is change