On viscous flow and azimuthal anisotropy of the quark-gluon plasma in a strong magnetic field

We calculate the viscous pressure tensor of the quark-gluon plasma in a strong magnetic field. It is azimuthally anisotropic and is characterized by five shear viscosity coefficients, four of which vanish when the field strength eB is much larger than the plasma temperature squared. We argue that the azimuthally anisotropic viscous pressure tensor generates the asymmetric transverse flow. As an illustration, we consider non-relativistic plasma flow in a very strong constant magnetic field; azimuthal asymmetry in this case is as large as 1/3, even not taking into account the collision geometry. This result suggests that the magnitude of the shear viscosity extracted from the experimental data ignoring the magnetic field must be underestimated, although a more quantitative estimate warrants further numerical investigation.