Shear Viscosity of a Gluon Plasma in Perturbative QCD
Jiunn-Wei Chen, Hui Dong, Kazuaki Ohnishi, Qun Wang
备注：
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 clarification
We calculate the shear viscosity $η$ to entropy density $s$ ratio $η/s$ of a gluon plasma in kinetic theory including the gg->gg and gg<->ggg processes. Due to the suppressed contribution to $η$ in the gg->gg forward scattering, it is known that the gluon bremsstrahlung gg<->ggg process also contributes at the same order $O(α_{s}^{-2})$ in perturbative QCD. Using the Gunion-Bertsch formula for the gg<->ggg 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 gg<->ggg contribution becomes more important to $η$ than gg->gg for $α_{s}\gtrsim 2\times 10^{-3}$. Therefore, at $α_{s}=0.1$, $η/s\simeq 1.0$, 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 gg<->ggg 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.
One of the most remarkable features of the Quark Gluon Plasma is its nearly perfect fluidity behavior indicated by the small shear viscosity to entropy density ratio obtained from fitting relativistic viscous hydrodynamics flow harmonics to experimental data. In recent years, bulk viscosity has also been considered in the context of event-by-event relativistic hydrodynamics and it has been found to have a non-trivial interplay with shear viscosity. In this paper some of the issues are discussed that require further work when extracting the shear viscosity to entropy density ratio in the presen…
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Influence of a temperature-dependent shear viscosity on the azimuthal asymmetries of transverse momentum spectra in ultrarelativistic heavy-ion collisions
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