No radiative generation of Chern-Simons-like term in Lorentz-violating QED: dealing with IR divergences

Abstract

The issue intensively claimed in the literature on the generation of a CPT-odd and Lorentz violating Chern-Simons-like term by radiative corrections owing to a CPT violating interaction -- the axial coupling of fermions with a constant vector field $b_\m$ -- is mistaken. The presence of massless gauge field triggers IR divergences that might show up from the UV subtractions, therefore, so as to deal with the (actual physical) IR divergences, the Lowenstein-Zimmermann subtraction scheme, in the framework of BPHZL renormalization method, has to be adopted. The proof on the non generation of such a Chern-Simons-like term is done, independent of any kind of regularization scheme, at all orders in perturbation theory.

In honor of Prof. Manfred Schweda (1939-2017). Work presented at the XXXVIII National Meeting on Particle Physics and Fields, September 18-22, 2017 - Passa Quatro - Minas Gerais - Brazil. Reference [46] corrected

References in corpus (4)

• Gauge Invariance and the Pauli-Villars Regulator in Lorentz- and CPT-Violating Electrodynamics
• Gauge invariance and the CPT and Lorentz violating induced Chern-Simons-like term in extended QED
• The ambiguity-free four-dimensional Lorentz-breaking Chern-Simons action
• Extended QED with CPT violation : clarifying some controversies