Shear viscosity to entropy density ratio of QCD below the deconfinement temperature

Using chiral perturbation theory we investigate the QCD shear viscosity (eta) to entropy density (s) ratio below the deconfinement temperature (similar to 170 MeV) with zero baryon number density. It is found that eta/s of QCD is monotonically decreasing in temperature (T) and reaches 0.6 with estimated similar to 50% uncertainty at T = 120 MeV. A naive extrapolation of the leading order result shows that eta/s reaches the 1/4 pi minimum bound proposed by Kovtun, Son, and Starinets using string theory methods at T similar to 200 MeV. This suggests a phase transition or cross over might occur at T less than or similar to 200 MeV in order for the bound to remain valid. Also, it is natural for eta/s to stay close to the minimum bound around the phase transition temperature as was recently found in heavy ion collisions. (c) 2007 Elsevier B.V. All rights reserved.