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

TL;DR

This paper proves that a Chern-Simons-like term cannot be generated radiatively in Lorentz-violating QED due to IR divergences, using a regularization-independent approach within the BPHZL renormalization framework.

Contribution

It demonstrates, at all orders, that no CPT-odd Lorentz-violating Chern-Simons-like term arises from radiative corrections in Lorentz-violating QED, addressing IR divergence issues.

Findings

No radiative generation of Chern-Simons-like term in Lorentz-violating QED.

IR divergences are properly handled using BPHZL renormalization.

The proof is regularization-independent and valid at all perturbative orders.

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.