Competition between magnetic catalysis effect and chiral rotation effect

TL;DR

This paper investigates how magnetic catalysis and chiral rotation effects compete in a parallel electromagnetic field within the NJL model, revealing complex mass gap behaviors influenced by magnetic and electric fields.

Contribution

It introduces a detailed analysis of the competition between magnetic catalysis and chiral rotation effects, identifying a critical electric field affecting the mass gap behavior.

Findings

Mass gap exhibits three different behaviors with increasing magnetic field.

A critical electric field of approximately 86.4 MeV is identified.

The critical electric field is independent of temperature and chemical potential.

Abstract

In this work, we explore the competition between magnetic catalysis effect and chiral rotation effect in a general parallel electromagnetic field within the effective Nambu--Jona-Lasinio model. For a given electric field $E$ at zero temperature, the mass gap shows three different features with respect to an increasing magnetic field $B$: increasing monotonically, decreasing after increasing and decreasing monotonically. By making use of strong magnetic field approximation, we illuminate that this is due to the competition between catalysis effect and chiral rotation effect induced both by the magnetic field, and a critical electric field $\sqrt{eE_c}=86.4~{\rm MeV}$ is found beyond which the mass gap will eventually decrease at large $B$. As only large magnetic field is relevant for the derivation, the critical electric field does not depend on the temperature $T$ or chemical potential $\mu$.