Shear viscosity of the Quark-Gluon Plasma from a virial expansion

Abstract

We calculate the shear viscosity $\eta$ in the quark-gluon plasma (QGP) phase within a virial expansion approach with particular interest in the ratio of $\eta$ to the entropy density $s$, i.e. $\eta /s$. The virial expansion approach allows us to include the interactions between the partons in the deconfined phase and to evaluate the corrections to a single-particle partition function. In the latter approach we start with an effective interaction with parameters fixed to reproduce thermodynamical quantities of QCD such as energy and/or entropy density. We also directly extract the effective coupling ${\text{ga}}_{\mathrm{V}}$ for the determination of $\eta$. Our numerical results give a ratio $\eta /s\approx 0.097$ at the critical temperature $T_{\mathrm{c}}$, which is very close to the theoretical bound of $1/(4\pi )$. Furthermore, for temperatures $T\le 1.8T_{\mathrm{c}}$ the ratio $\eta /s$ is in the range of the present experimental estimates $0.1-0.3$ at RHIC. When combining our results for $\eta /s$ in the deconfined phase with those from chiral perturbation theory or the resonance gas model in the confined phase we observe a pronounced minimum of $\eta /s$ close to the critical temperature $T_{\mathrm{c}}$.

Comments: Published in Eur. Phys. J. C, 7 pages, 2 figures, 3 table