Chirality imbalance and chiral magnetic effect under a parallel electromagnetic field

TL;DR

This paper analytically investigates the evolution of chirality imbalance and the chiral magnetic effect under parallel electromagnetic fields, revealing their dependence on electric field strength and their persistence after field removal.

Contribution

It provides analytical solutions for the Dirac equation with time-dependent electric and constant magnetic fields, elucidating the dynamical origin of chirality imbalance without artificial sources.

Findings

Chirality imbalance and CME current increase with electric field strength.

Both quantities remain finite after the electric field is turned off.

A simple relation between chirality imbalance and fermion pair-production rate is established.

Abstract

We study the time evolution of the chirality imbalance $n_5$ and the chiral magnetic effect (CME) under the external parallel electromagnetic fields without assuming the artificial chiral asymmetric source. We adopt the time-dependent Sauter-type electric and constant magnetic field, and obtain analytical solutions of the Dirac equation for a massive fermion. We use the point-split regularization to calculate the vacuum contribution in the gauge invariant way. As a result, we find that $n_5$ and CME current increase substantially as the electric field increases, and stay finite after the electric field is switched off. The chirality imbalance and CME current are shown to consist of a dominant contribution, which is essentially proportional to relativistic velocity, and a small oscillating part. We find a simple analytical relation between $n_5$ and the fermion pair-production rate from the vacuum. We also discuss dynamical origin of the chirality imbalance in detail.