Low-Shear QCD Plasma from Perturbation Theory

We argue that the inferred ratio of shear viscosity to entropy density of the quark-gluonplasma, h/s < 0.5 near the deconfinement temperature Tc, can be understood from perturbative QCD.To rebut opposite views, we first show that the existing leading order result should not be expandedin logarithms. After then settling the question of scale for the running coupling, we establish atemperature dependence of h/s which agrees well with constraints from hydrodynamics.