Transport Coefficient of Gluon Plasma from Lattice QCD

TL;DR

This study calculates the shear and bulk viscosities of gluon plasma using lattice QCD simulations across a wide temperature range, finding results consistent with perturbative calculations at high temperatures and satisfying the KSS bound.

Contribution

First lattice QCD calculation of gluon plasma transport coefficients over a broad temperature range, including near the transition, with analysis of spectral function effects.

Findings

Shear viscosity $\\eta$ is smaller than hadron masses near transition.

Bulk viscosity is consistent with zero across studied temperatures.

The ratio $\eta/s$ satisfies the KSS bound, around 0.1-0.4 for $T/T_c<3$.

Abstract

In this report we present our calculation of the transport coefficient of gluon system on $24^3\times 8$ lattice in the quench approximation. Simulations are carried out in the range, $1.4 \le T/T_c \le 24$. In the temperature region slightly above the transition, where the perturbative calculation is not applicable, the shear viscosity($\eta$) is smaller than typical hadron masses. The bulk viscosity is consistent with zero within the range of error bars in $1.4 \le T/T_c \le 24$. We compare our results with the perturbative calculations in large $T/T_c$ region. It is found that the lattice and perturbative results are consistent with each other there. The ratio $\eta/s$ is around $0.1-0.4$ in $T/T_c < 3$ region and satisfies the KSS bound\cite{KSS}. In order to estimate the contribution from high frequency part of the spectral function, we study the effects of a term $\rho^{high}$ proposed by Aarts and Resco\cite{Aarts}. It is found that until the threshold mass becomes small, its effect is quite small, and that viscosity decreases as the threshold decreases. From these studies we think that although our result is obtained under an assumptions for the spectral function, it gives a reasonable estimation for $\eta$($=\pi d\rho/d\omega$ at $\omega=0$), and qualitative results will not be changed when the accurate spectral function is obtained.