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

In this paper, we investigate a Lorentz symmetry breaking extension of Quantum Electrodynamics (QED), incorporating five-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.