Shear and Bulk Viscosities of a Weakly Coupled Quark Gluon Plasma with Finite Chemical Potential and Temperature---Leading-Log Results

TL;DR

This paper computes shear and bulk viscosities of a weakly coupled quark-gluon plasma at finite temperature and chemical potential, revealing how these properties vary with chemical potential, flavor number, and implications for QCD's fluidity.

Contribution

It provides leading-log order calculations of viscosities at finite mu and T, highlighting their dependence on chemical potential and flavor number, and suggests conditions for minimal viscosity in QCD.

Findings

eta/s increases with mu, scales as (mu/T)^2 at large mu

zeta/s is insensitive to mu

eta/s decreases with increasing N_f for N_f ≥ 2

Abstract

We calculate the shear (eta) and bulk (zeta) viscosities of a weakly coupled quark gluon plasma at the leading-log order with finite temperature T and quark chemical potential mu. We find that the shear viscosity to entropy density ratio eta/s increases monotonically with mu and eventually scales as (mu/T)^2 at large mu. In contrary, zeta/s is insensitive to mu. Both eta/s and zeta/s are monotonically decreasing functions of the quark flavor number N_f when N_f \geq 2. This property is also observed in pion gas systems. Our perturbative calculation suggests that QCD becomes the most perfect (i.e. with the smallest eta/s) at mu=0 and N_f = 16 (the maximum N_f with asymptotic freedom). It would be interesting to test whether the currently smallest eta/s computed close to the phase transition with mu=0 and N_f = 0 can be further reduced by increasing N_f.