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How Perfect a Gluon Plasma Can Be in Perturbative QCD?
The shear viscosity to entropy density ratio, \eta /s, characterizes how
perfect a fluid is. We calculate the leading order \eta /s of a gluon plasma in
perturbation using the kinetic theory. The leading order contribution only
involves the elastic gg -> gg (22) process and the inelastic ggggg (23)
process. The Hard-Thermal-Loop (HTL) treatment is used for the 22 matrix
element, while the exact matrix element in vacuum is supplemented by the gluon
Debye mass insertion for the 23 process. Also, the asymptotic mass is used for
the external gluons in the kinetic theory. The errors from not implementing HTL
and the Landau-Pomeranchuk-Migdal effect in the 23 process, and from the
uncalculated higher order corrections, are estimated. Our result for \eta /s
lies between that of Arnold, Moore and Yaffe (AMY) and Xu and Greiner (XG). Our
result shows that although the finite angle contributions are important at
intermediate \alpha_s (\alpha_s \sim 0.01-0.1), the 22 process is still more
important than 23 when \alpha_s < 0.1. This is in qualitative agreement with
AMY'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
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