Effective interaction of Chern-Simons boson with fermions

TL;DR

This paper investigates a Chern-Simons vector boson extension of the Standard Model, analyzing its loop-induced interactions with fermions, revealing nonrenormalizable behavior for same-flavor interactions and deriving an effective low-energy Lagrangian.

Contribution

It introduces a new massive vector boson with loop-induced interactions, analyzing their renormalizability and deriving an effective interaction Lagrangian at low energies.

Findings

Divergent contributions for same-flavor fermion interactions do not cancel, indicating nonrenormalizability.

Interactions involving different-flavor fermions are finite and well-defined.

The effective Lagrangian resembles a Z' boson interaction with SM fermions.

Abstract

We consider a vector extension of the Standard Model (SM) with a Chern-Simons-type interaction. This extension introduces a new massive vector boson (the Chern-Simons (CS) boson) that does not couple directly to SM fermions at tree level. We analyze the effective loop-induced interaction of this new vector boson with SM fermions and study its renormalizability in the $R_\xi$ gauge. We find that, in the effective interaction between the CS boson and same-flavor fermions, the divergent contributions from individual loop diagrams do not cancel when all relevant diagrams are taken into account. In contrast, for interactions involving fermions of different flavors, the corresponding loop-induced contributions are finite and well defined. This indicates that, in the low-energy limit, the theory exhibits nonrenormalizable behavior in the sector describing the loop-induced interaction of the CS boson with same-flavor fermions. The interaction terms between the CS boson and same-flavor fermions, characterized by divergent coefficients, are identified and must be treated within the framework of effective field theory. Finally, we derive the leading-order effective Lagrangian describing the interaction of a GeV-scale CS boson with SM fermions and discuss the number of independent parameters entering this Lagrangian. The leading-order interaction we obtained turns out to be similar to the interaction of a $Z^\prime$ boson with SM fermions.