Chiral asymmetry and axial anomaly in magnetized relativistic matter

TL;DR

This paper investigates how the chiral shift parameter affects the axial current and anomaly in magnetized relativistic matter, demonstrating its presence in the normal phase and its impact on axial current without altering the anomaly relation.

Contribution

It shows that the chiral shift parameter exists in the normal phase under magnetic fields and modifies the axial current while preserving the anomaly relation.

Findings

The chiral shift parameter Delta necessarily exists in the normal phase.

Delta modifies the axial current's form but not the axial anomaly relation.

The results are consistent across different regularization schemes.

Abstract

The induced axial current and the chiral anomaly are studied in the normal phase of magnetized relativistic matter. A special attention is paid to the role of the chiral shift parameter Delta, leading to a relative shift of the longitudinal momenta in the dispersion relations of opposite chirality fermions. In the Nambu-Jona-Lasinio model, it is shown directly from the form of the gap equation that Delta necessarily exists in the normal phase in a magnetic field. By making use of the gauge invariant point-splitting regularization, we then show that the presence of Delta essentially modifies the form of the axial current, but does not affect the conventional axial anomaly relation. By recalculating the axial current with the proper-time regularization, we conclude that the result is robust with respect to a specific regularization scheme used.