Magnetic helicity in plasma of chiral fermions electroweakly interacting with inhomogeneous matter

TL;DR

This paper investigates how chiral fermions interacting with inhomogeneous matter influence magnetic helicity, deriving kinetic equations and applying findings to astrophysical phenomena like neutron stars and pulsars.

Contribution

It introduces a new approach to modeling chiral fermions in nonuniform matter using Berry phase, and applies this to astrophysical contexts to analyze magnetic helicity evolution.

Findings

Derived effective action and kinetic equations for chiral particles.

Found correction to electric current and Adler anomaly in rotating matter.

Estimated magnetic helicity change rate in neutron stars matching pulsar cycles.

Abstract

We study chiral fermions electroweakly interacting with a background matter having the nonuniform density and the velocity arbitrarily depending on coordinates. The dynamics of this system is described approximately by finding the Berry phase. The effective action and the kinetic equations for right and left particles are derived. In the case of a rotating matter, we obtain the correction to the anomalous electric current and to the Adler anomaly. Then we study some astrophysical applications. Assuming that the chiral imbalance in a rotating neutron star vanishes, we obtain the rate of the magnetic helicity change owing to the interaction of chiral electrons with background neutrons. The characteristic time of the helicity change turns out to coincide with the period of the magnetic cycle of some pulsars.