Small shear viscosity in the semi quark gluon plasma

TL;DR

This paper calculates the shear viscosity of the semi quark-gluon plasma near the deconfinement transition, showing it is suppressed by the Polyakov loop, with implications for heavy quark behavior in heavy-ion collisions.

Contribution

It introduces a semiclassical approach to compute shear viscosity in the semi-QGP, accounting for the Polyakov loop's effect on colored particle densities.

Findings

Shear viscosity is suppressed by two powers of the Polyakov loop near T_c.

Colored particle densities decrease according to their color representation.

Suppression pattern may explain charm quark behavior at RHIC.

Abstract

At nonzero temperature in QCD, about the deconfining phase transition there is a "semi" quark gluon plasma (semi-QGP), where the expectation value of the (renormalized) Polyakov loop is less than one. This can be modeled by a semiclassical expansion about a constant field for the vector potential, A_0, which is diagonal in color. We compute the shear viscosity in the semi-QGP by using the Boltzmann equation in the presence of this background field. To leading, logarithmic order in weak coupling, the dominant diagrams are given by the usual scattering processes of 2 -> 2 particles. For simplicity we also assume that both the number of colors and flavors are large. Near the critical temperature T_c, where the expectation value of the Polyakov loop is small, the overall density of colored fields decreases according to their color representation, with the density of quarks vanishes linearly with the loop, and that of gluons, quadratically. This decrease in the overall density dominates changes in the transport cross section. As a result, relative to that in the perturbative QGP, near T_c the shear viscosity in the semi-QGP is suppressed by two powers of the Polyakov loop. In a semiclassical expansion, the suppression of colored fields depends only upon which color representation they lie in, and not upon their mass. That light and heavy quarks are suppressed in a common manner may help to explain the behavior of charm quarks at RHIC.