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

TL;DR

This paper calculates the longitudinal electrical conductivity in perturbative QCD under strong magnetic fields, revealing its dependence on quark mass and magnetic field strength, and discusses implications for color charge transport and sphaleron transitions.

Contribution

It provides a complete leading order calculation of longitudinal conductivity in strong magnetic fields using an effective kinetic theory with Landau level quarks and collision terms from 1-to-2 processes.

Findings

Longitudinal conductivity scales as e^2(eB)T/(\alpha_s m_q^2\log(m_q/T)) in small quark mass regime.

Longitudinal color conductivity is enhanced by strong magnetic fields.

Sphaleron transition rate is suppressed due to increased color conductivity under strong magnetic fields.

Abstract

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. We observe that the longitudinal color conductivity is enhanced by strong magnetic field, which implies that the sphaleron transition rate in perturbative QCD is suppressed by strong magnetic field due to the enhanced Lenz's law in color field dynamics.