Longitudinal Conductivity in Strong Magnetic Field in Perturbative QCD: Complete Leading Order

Understand

We compute the longitudinal electrical conductivity in the presence of strong background magnetic field in complete leading order of perturbative QCD, based on the assumed hierarchy of scales $\alpha_s eB\ll (m_q^2,T^2)\ll eB$.

• We formulate an effective kinetic theory of lowest Landau level quarks with the leading order QCD collision term arising from 1-to-2 processes that become possible due to 1+1 dimensional Landau level kinematics.
• In small $m_q/T\ll 1$ regime, the longitudinal conductivity behaves as $\sigma_{zz}\sim e^2(eB)T/(\alpha_s m_q^2\log(m_q/T))$, where the quark mass dependence can be understood from the chiral anomaly with the axial charge relaxation provided by a finite quark mass $m_q$.
• We also present parametric estimates for the longitudinal and transverse "color conductivities" in the presence of strong magnetic field, by computing dominant damping rates for quarks and gluons that are responsible for color charge transportation.