Shear Viscosity of a Gluon Plasma in Perturbative QCD
Journal
Physics Letters
Journal Volume
B685
Pages
277-282
Date Issued
2009-07
Author(s)
Abstract
We calculate the shear viscosity (η) to entropy density (s) ratio η / s of a gluon plasma in kinetic theory including the g g → g g and g g → g g g processes. Due to the suppressed contribution to η in the g g → g g forward scattering, it is known that the gluon bremsstrahlung g g ↔ g g g process also contributes at the same order (O (αs- 2)) in perturbative QCD. Using the Gunion-Bertsch formula for the g g → g g g 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 g g ↔ g g g contribution becomes more important to η than g g → g g for αs ≳ 2 × 10- 3. Therefore, at αs = 0.1, η / s ≃ 1.0, between 2.7 obtained by Arnold, Moore and Yaffe (AMY) and 0.5 obtained by Xu and Greiner (XG). 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 g g ↔ g g g process is about 10-30% of the total which is close to AMY's prediction. This shows that further studies beyond the soft bremsstrahlung approximation used by XG and collinear approximation used by AMY are needed. © 2010 Elsevier B.V. All rights reserved.
Type
journal article