New constraints on the 3-3-1 model with right-handed neutrinos

TL;DR

This paper investigates the 3-3-1 model with right-handed neutrinos, analyzing symmetry breaking patterns and their implications for Nambu-Goldstone bosons, ultimately proposing a minimal soft-breaking solution to avoid astrophysical constraints.

Contribution

It identifies the problematic NG bosons in the model and introduces a minimal soft $ ext{Z}_2$-breaking term to eliminate them while preserving model simplicity.

Findings

Model with $ ext{Z}_2$ symmetry is excluded due to NG boson emission.

A unique soft $ ext{Z}_2$-breaking term removes problematic NG bosons.

The proposed solution maintains the model's minimal scalar sector.

Abstract

In the framework of a 3-3-1 model with right-handed neutrinos and three scalar triplets we consider different spontaneous symmetry breaking patterns seeking for a non-linear realization of accidental symmetries of the model, which will produce physical Nambu-Goldstone (NG) bosons in the neutral scalar spectrum. We make a detailed study of the safety of the model concerning the NG boson emission in energy loss processes which could affect the standard evolution of astrophysical objects. We consider the model with a $\mathbb{Z}_2$ symmetry, conventionally used in the literature, finding that in all of the symmetry breaking patterns the model is excluded. Additionally, looking for solutions for that problem, we introduce soft $\mathbb{Z}_2$-breaking terms in the scalar potential in order to remove the extra accidental symmetries and at the same time maintain the model as simple as possible. We find that there is only one soft $\mathbb{Z}_2$-violating term that can get rid of the problematic NG bosons.