Shear Viscosity of Collider-Produced QCD Matter I: AMY Formalism vs. A Modified Relaxation Time Approximation in 0-flavor SU(3) Theory

The AMY formalism is widely used to describe the transport coefficients of asymptotically hot and dense QCD matter, such as shear viscosity $\eta$. In literature prior to AMY, the viscosity of an asymptotically hot QCD plasma was expressed by a $q^2$ momentum transfer-weighted relaxation time approximation. Recent studies that compared numerical transport calculations and analytical expressions for $\eta$ demonstrated that asymptotically high temperatures and densities induce anisotropic scatterings, which are exhibited in the quark-gluon plasma produced by relativistic heavy ion collisions. In these studies, the QGP was treated as a Maxwell-Boltzmann-distributed gluon gas with added (anti-)quark degrees of freedom. One such method used in the comparison was the ``modified'' $q^2$ transport-weighted RTA. In this study, a comparison between the AMY formalism (both numerical calculations and next-leading-log expression) and the modified RTA expression for $\eta$ is made in 0-flavor SU(3) theory for collider-produced QGP. The comparison between numerical AMY calculations and the modified RTA method shows perfect agreement under the temperatures relevant for collider-produced QGP. Additionally, AMY is compared with the Chapman-Enskog method, which is well understood to better describe anisotropic collider-produced QGP.