Shear viscosity of the quark-gluon plasma in a weak magnetic field in perturbative QCD: Leading log

We compute the shear viscosity of two-flavor QCD plasma in an external magnetic field in perturbative QCD at leading log order, assuming that the magnetic field is weak or soft: eB similar to g(4) log (1/g)T-2. We work in the assumption that the magnetic field is homogeneous and static, and the electrodynamics is nondynamical in a formal limit e -> 0 while eB is kept fixed. We show that the shear viscosity takes a form eta = (eta) over bar((B) over bar )T-3 / (g(1) log(1/g)) with a dimensionless function (eta) over bar((B) over bar) in terms of a dimensionless variable (B) over bar = (e B)/(g(4) log(1/g)T-2. The variable (B) over bar corresponds to the relative strength of the effect of cyclotron motions compared to the QCD collisions: (B) over bar similar to l(mfp)/l(cyclo). We provide a full numerical result for the scaled shear viscosity (eta) over bar((B) over bar).