Dielectric correction to the chiral magnetic effect

Abstract

We derive an electric current density $j_{em}$ in the presence of a magnetic field $B$ and a chiral chemical potential $\mu_5$. We show that $j_{em}$ has not only the anomaly-induced term $\propto \mu_5 B$ (i.e. Chiral Magnetic Effect) but also a non-anomalous correction which comes from interaction effects and expressed in terms of the susceptibility. We find the correction characteristically dependent on the number of quark flavors. The numerically estimated correction turns out to be a minor effect on heavy-ion collisions but can be tested by the lattice QCD simulation.