Theoretical constraints on the couplings of non-exotic minimal $Z'$ bosons

TL;DR

This paper combines unitarity and renormalisation group methods to derive new, stronger constraints on gauge couplings in minimal $Z'$ models, refining existing triviality bounds and analyzing their evolution.

Contribution

It introduces a novel approach using perturbative unitarity and RG equations to constrain gauge couplings in minimal $Z'$ models, providing more precise bounds than traditional triviality limits.

Findings

Perturbative unitarity imposes stronger bounds than triviality.

The method refines triviality bounds in benchmark $Z'$ models.

Analysis includes gauge coupling evolution and model structure in Feynman gauge.

Abstract

We have combined perturbative unitarity and renormalisation group equation arguments in order to find a dynamical way to constrain the space of the gauge couplings ($g'_1$, $\widetilde{g}$) of the so-called "Minimal $Z'$ Models". We have analysed the role of the gauge couplings evolution in the perturbative stability of the two-to-two body scattering amplitudes of the vector and scalar sectors of these models and we have shown that perturbative unitarity imposes an upper bound that is generally stronger than the triviality constraint. We have also demonstrated how this method quantitatively refines the usual triviality bound in the case of benchmark scenarios such as the $U(1)_\chi$, the $U(1)_R$ or the "pure" $U(1)_{B-L}$ extension of the Standard Model. Finally, a description of the underlying model structure in Feynman gauge is provided.