Shear Viscosity of Quark-Gluon Plasma in 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: $eB\sim g^4\log (1/g)T^2$. We show that the shear viscosity takes a form $\eta =\bar{\eta }(\bar{B})T^3/(g^4\log (1/g))$ with a dimensionless function $\bar{\eta }(\bar{B})$ in terms of a dimensionless variable $\bar{B}=(eB)/(g^4\log (1/g)T^2)$. The variable $\bar{B}$ corresponds to the relative strength of the effect of cyclotron motions compared to the QCD collisions: $\bar{B}\sim l_{mfp}/l_{cyclo}$. We provide a full numerical result for the scaled shear viscosity $\bar{\eta }(\bar{B})$.

Comments: 27 pages, 2 figures, updated reference list, discussion added, published version