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 ∆, 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 ∆ 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 ∆ 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.
Physics Letters B
- Pub Date:
- January 2011
- High Energy Physics - Phenomenology;
- High Energy Physics - Theory;
- Nuclear Theory
- 7 pages, published version: several refferences added and discussions extended