Shear Viscosity of a Quark Plasma Near the Chiral Phase Transition

We calculate the shear viscosity $\eta$ of a quark plasma through the two-flavor Nambu-Jona-Lasinio (NJL) model in the chiral limit, at finite temperature $T$, and baryon number chemical potential $\mu_B$. We solve the Boltzmann equation by using in the collision term cross sections that are correct to leading order in the coupling constant. We find the ratio of shear viscosity to entropy density above and slightly below the chiral transition temperature to vary from 1.5 to 13 times the conjectured lower bound of $(4\pi)^{-1}$ depending on the chemical potential to temperature ratio. Ratio of shear viscosity to entropy density is found to be a monotonically increasing function of the ratio of chemical potential to temperature for temperatures between 185 and 300 MeV.