The shear viscosity of parton matter under anisotropic scatterings

TL;DR

This paper analytically and numerically investigates the shear viscosity of quark-gluon plasma, confirming the Chapman-Enskog method's accuracy and analyzing how shear viscosity to entropy ratio evolves in heavy-ion collision simulations.

Contribution

It demonstrates the agreement of Chapman-Enskog with Green-Kubo methods for anisotropic scatterings and applies this to study shear viscosity in realistic heavy-ion collision scenarios.

Findings

Chapman-Enskog method agrees with Green-Kubo for anisotropic scatterings

Shear viscosity to entropy ratio increases over time with constant cross section

Parton matter exhibits a very small η/s ratio, close to 1/(4π), in simulations

Abstract

The shear viscosity $\eta$ of a quark-gluon plasma in equilibrium can be calculated analytically using multiple methods or numerically using the Green-Kubo relation. It has been realized, which we confirm here, that the Chapman-Enskog method agrees well with the Green-Kubo result for both isotropic and anisotropic two-body scatterings. We then apply the Chapman-Enskog method to study the shear viscosity of the parton matter from a multi-phase transport model. In particular, we study the parton matter in the center cell of central and midcentral Au+Au collisions at $200A$ GeV and Pb+Pb collisions at $2760A$ GeV, which is assumed to be a plasma in thermal equilibrium but partial chemical equilibrium. As a result of using a constant Debye mass or cross section $\sigma$ for parton scatterings, the $\eta/s$ ratio increases with time (as the effective temperature decreases), contrary to the trend preferred by Bayesian analysis of the experimental data or pQCD results that use temperature-dependent Debye masses. At $\sigma=3$ mb that enables the transport model to approximately reproduce the elliptic flow data of the bulk matter, the average $\eta/s$ of the parton matter in partial equilibrium is found to be very small, between one to two times $1/(4\pi)$.