Ambiguities in the generation of CFJ-terms in a QED with dimension-5 operators in one loop

Abstract

In this paper, we investigate a Lorentz symmetry breaking extension of Quantum Electrodynamics (QED), incorporating 5-dimensional CPT-odd terms at the one-loop level. Employing an independent regularization method, we systematically separate the divergences into regularization-independent contributions and regularization-dependent (surface terms). We demonstrate that these surface terms, potentially contributing to the radiative generation of Carroll-Field-Jackiw (CFJ) terms, remain undetermined even when imposing the Ward-Takahashi identity. Our results are consistent with existing literature and emphasize the necessity of a careful and consistent treatment of regularization ambiguities in quantum field theories involving symmetry breaking extensions.