Viscosities of Hot Gluon -- A Lattice QCD Study --

TL;DR

This study calculates the shear and bulk viscosities of a gluon system using lattice QCD across a wide temperature range, providing insights into the properties of the quark-gluon plasma observed in RHIC experiments.

Contribution

It presents the first lattice QCD calculations of gluon transport coefficients over a broad temperature spectrum, including RHIC and high-temperature regimes.

Findings

/s ratio is 0.1-0.4 near RHIC temperatures, satisfying the KSS bound.

Viscosities increase by two to three orders of magnitude at higher temperatures.

Results are limited by the quench approximation and spectral function ansatz.

Abstract

We present transport coefficients (shear viscosity, $\eta$, and bulk viscosity, $\zeta$) for the gluon system obtained by the lattice QCD. This is an indispensable calculation towards the understanding of ``New State of Matter'' observed in RHIC. We study the temperature regions of RHIC ($1.4 \leq T/T_c \leq 1.8$) and much higher ones up to $ T/T_c \sim 20$. In RHIC regions, the ratio of shear viscosity to entropy density, $\eta/s$, is around $\sim 0.1-0.4$, and satisfies the KSS bound. At high temperature, $\eta$ becomes two or three oder of magnitude larger. Our calculation has two limitations: (i) the use of the quench approximation, i.e., without quark pair creation-annihilation effects on vacuum, and (ii) the use of an ansatz for the spectral function. The first point has been well studied in calculations of the spectroscopy and the phase-transition behavior. To investigate the second point, we compare our results with perturbative calculations in high $T$-regions, and also check the effects of the modification of the spectral function on the viscosity.