Suppression of the shear viscosity in a “semi”-quark-gluon plasma

Abstract

We consider QCD at temperatures $T$ near ${T}_{c}$, where the theory deconfines. We distinguish between a ``complete'' quark-gluon plasma (QGP), where the vacuum expectation value of the renormalized Polyakov loop is near unity, essentially constant with $T$, and the ``semi''-QGP, where the loop changes strongly with $T$. Lattice simulations indicate that in QCD, there is a semi-QGP from below ${T}_{c}$ to a few times that. Using a semiclassical model, we compute the shear viscosity, $\ensuremath{\eta}$, to leading order in perturbation theory. We find that near ${T}_{c}$, where the expectation value of the Polyakov loop is small, that $\ensuremath{\eta}/{T}^{3}$ is suppressed by two powers of the loop. For heavy ions, this suggests that during the initial stages of the collision, hydrodynamic behavior at the LHC will be characterized by a shear viscosity which is significantly larger than that at RHIC.