Divergences in the Effective Loop Interaction of the Chern–Simons Bosons with Leptons. The Unitary Gauge Case

We will consider the extension of the Standard Model (SM) with Chern–Simons type interaction. This extension has a new vector massive boson (Chern–Simons bosons). There is no direct interaction between the Chern–Simons bosons and fermions of the SM. Using only threeparticle dimension-4 interaction of the Chern–Simons bosons with vector bosons of the SM, we consider effective loop interaction of a new vector boson with leptons. We consider the renormalizability of this loop interaction and conclude that, for the computation of loop diagrams in the unitary gauge, we can not eliminate the divergences in the effective interaction of the Chern–Simons bosons with leptons.