Shear viscosity coefficient and relaxation time of causal dissipative hydrodynamics in QCD

TL;DR

This paper calculates the shear viscosity coefficient and relaxation time in causal dissipative hydrodynamics within QCD, showing their relation to microscopic formulas and simplifying assumptions in leading order calculations.

Contribution

It derives a compact formula for shear viscosity and relaxation time in causal hydrodynamics, applying it to QCD and chiral perturbation theory, linking these coefficients to microscopic theory.

Findings

Shear viscosity reduces to Green-Kubo-Nakano formula in leading order.

Relaxation time is proportional to shear viscosity divided by pressure.

The formulas are validated within QCD and chiral perturbation theory.

Abstract

The shear viscosity coefficient and the corresponding relaxation time for causal dissipative hydrodynamics are calculated based on the microscopic formula proposed in [T. Koide and T. Kodama, Phys. Rev. \textbf{E 78}, 051107 (2008)]. Here, the exact formula is transformed into a more compact form and applied it to evaluate these transport coefficients in the chiral perturbation theory and perturbative QCD. It is shown that in the leading order calculation, the causal shear viscosity coefficient $\eta$ reduces to that of the ordinary Green-Kubo-Nakano formula, and the relaxation time $\tau_{\pi}$ is related to $\eta$ and pressure $P$ by a simple relationship, $\tau_{\pi}=\eta/P$.