Divergences in the effective loop interaction of the Chern-Simons bosons with leptons. The unitary gauge case

TL;DR

This paper investigates the loop interactions of Chern-Simons bosons with leptons within an extended Standard Model, revealing divergences in the effective interaction when computed in the unitary gauge.

Contribution

It analyzes the divergences in the loop interactions of Chern-Simons bosons with leptons, highlighting issues in renormalizability in the unitary gauge.

Findings

Divergences appear in the effective interaction calculations.

Renormalizability issues are identified in the unitary gauge.

Loop diagrams cannot be rendered divergence-free in this setup.

Abstract

In this paper, we consider the extension of the Standard Model with Chern-Simons type interaction. There is a new vector massive boson (Chern-Simons bosons) in this extension. Using only three-particle 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 case of computation of loop diagrams in the unitary gauge, we can not get rid of the divergences in the effective interaction of the Chern-Simons bosons with leptons.