Shear viscosity of quark matter at finite temperature under an external magnetic field

We employ the diluted instanton liquid model and the Green-Kubo formula to investigate the shear viscosity of the SU(2) light-flavor quark matter at finite temperature under an external strong magnetic field e vertical bar B vertical bar similar to m(pi)(2). We apply the Schwinger method to calculate the effect of the external magnetic field. We find that the shear viscosity increases as temperature increases even beyond the transition temperature T-0 = 170 MeV if temperature-dependent model parameters are used. On the other hand, with temperature-independent ones the shear viscosity starts to drop when the temperature goes beyond T-0. Furthermore, we find that the presence of an external magnetic field will reduce the shear viscosity. However, this effect is almost negligible in the chiral-restored phase even for a very strong magnetic field, e vertical bar B vertical bar approximate to 10(20) gauss. We also compute the ratio of the shear viscosity and the entropy density eta/s and our results are well compatible with the other theoretical results for a wide temperature range. We also provide the parametrization of the temperature-dependent ratio eta/s from our numerical result as eta/s=0.27 - 0.87/t + 1.19/t(2) - 0.28/t(3) with t = T/T-0 for T=(100 similar to 350) MeV and e|B| = 0.