Chiral asymmetry and axial anomaly in magnetized relativistic matter

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 Δ, 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 Δ 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 Δ 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.