Shear Viscosity of a Gluon Plasma in Perturbative QCD

We calculate the shear viscosity $\eta$ to entropy density $s$ ratio $\eta /s$ of a gluon plasma in kinetic theory including the gg->gg and ggggg processes. Due to the suppressed contribution to $\eta$ in the gg->gg forward scattering, it is known that the gluon bremsstrahlung ggggg process also contributes at the same order $O(\alpha_{s}^{-2})$ in perturbative QCD. Using the Gunion-Bertsch formula for the ggggg matrix element which is valid for the limit of soft bremsstrahlung, we find that the result is sensitive to whether the same limit is taken for the phase space. Using the exact phase space, the ggggg contribution becomes more important to $\eta$ than gg->gg for $\alpha_{s}\gtrsim 2\times 10^{-3}$. Therefore, at $\alpha_{s}=0.1$, $\eta /s\simeq 1.0$, between 2.7 obtained by Arnold, Moore and Yaffe (AMY) and 0.5 obtained by Xu and Greiner. If the soft bremsstrahlung limit is imposed on the phase space such that the recoil effect from the bremsstrahlung gluon is neglected, then the correction from the ggggg process is about 10-30% of the total which is close to AMY's prediction. This shows that the soft bremsstrahlung approximation is not as good as previously expected.Comment: RevTex 4, 14 pages, 3 figures; The results for the soft bremsstrahlung limit for the phase space are added. The difference between AMY and XG approach is addressed with more clarificatio

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

Shear and Bulk Viscosities of a Gluon Plasma in Perturbative QCD: Comparison of Different Treatments for the gg<->ggg Process

The leading order contribution to the shear and bulk viscosities, \eta and \zeta, of a gluon plasma in perturbative QCD includes the gg -> gg (22) process, gg ggg (23) process and multiple scattering processes known as the Landau-Pomeranchuk-Migdal (LPM) effect. Complete leading order computations for \eta and \zeta were obtained by Arnold, Moore and Yaffe (AMY) and Arnold, Dogan and Moore (ADM), respectively, with the inelastic processes computed by an effective g gg gluon splitting. We study how complementary calculations with 22 and 23 processes and a simple treatment to model the LPM effect compare with the results of AMY and ADM. We find that our results agree with theirs within errors. By studying the contribution of the 23 process to \eta, we find that the minimum angle \theta among the final state gluons in the fluid local rest frame has a distribution that is peaked at \theta \sim \sqrt{\alpha_{s}}, analogous to the near collinear splitting asserted by AMY and ADM. However, the average of \theta is much bigger than its peak value, as its distribution is skewed with a long tail. The same \theta behavior is also seen if the 23 matrix element is taken to the soft gluon bremsstrahlung limit in the center-of-mass (CM) frame. This suggests that the soft gluon bremsstrahlung in the CM frame still has some near collinear behavior in the fluid local rest frame. We also generalize our result to a general SU(N_c) pure gauge theory and summarize the current viscosity computations in QCD.Comment: ReVTex 4, 18 pages, 7 figures, accepted version in Phys. Rev.

Bulk Viscosity of a Gas of Massless Pions

In the hadronic phase, the dominant configuration of QCD with two flavors of massless quarks is a gas of massless pions. We calculate the bulk viscosity (zeta) using the Boltzmann equation with the kinetic theory generalized to incorporate the trace anomaly. We find that the dimensionless ratio zeta/s, s being the entropy density, is monotonic increasing below T=120 MeV, where chiral perturbation theory is applicable. This, combined with previous results, shows that zeta/s reaches its maximum near the phase transition temperature Tc, while eta/s, eta being the shear viscosity, reaches its minimum near Tc in QCD with massless quarks.Comment: 12 pages, 1 figure; the version to appear in PR