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

Abstract

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∼g4log(1/g)T2. 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 η=η(B)T3/(g4log(1/g)) with a dimensionless function η(B) in terms of a dimensionless variable B=(eB)/(g4log(1/g)T2). The variable B corresponds to the relative strength of the effect of cyclotron motions compared to the QCD collisions: B∼lmfp/lcyclo. We provide a full numerical result for the scaled shear viscosity η(B).