Viscosity of a net-baryon fluid near the QCD critical point

In the dynamics of the QCD critical point, the net-baryon fluid, linked to the slow component of the order parameter, relaxes to a three-dimensional Ising system in equilibrium. An analytical study of shear and bulk viscosity, with constraints imposed by the dynamics of the critical net-baryon fluid, the universality property, and the requirements of a class of strong-coupling theories, is performed in the neighborhood of the critical point. It is found that the shear viscosity of the net-baryon fluid is restricted in the domain $1.6\le 4\pi \frac{\eta }{s}\le 3.7$ for $T_c<T\le 2T_c$, whereas the bulk viscosity is small, $4\pi \frac{\zeta }{s}<0.05$ (for $T>1.27T_c$), but rising towards the singularity at $T=T_c$.

Figure 1

Our solution of type I (continuous dark line) for the shear viscosity compared with the findings of Refs. [5] (open triangles), [23] (open circles), [24] (solid circles and solid triangles), [25] (open rectangles), [26] (dashed line), [27] (a quasiparticle model; band), and [6] (dotted line with solid rectangles). In the inset graph we focus on the shape of our solution in the vicinity of the critical temperature. Also solutions of type II (continuous light lines) are shown.

Figure 2

Solutions for the bulk viscosity (continuous lines) compared with the findings of Refs. [11] (dot-dashed line) and [28] (solid rectangles) with systematic (large) and statistical (small) uncertainties.