# Constraining the $3-3-1$ model with heavy neutral leptons using $(g-2)_{\mu}$ and dark matter observables

## TL;DR

This paper constrains the symmetry breaking scale of a 3-3-1 gauge model with heavy neutral leptons by analyzing muon anomalous magnetic moment and dark matter observables, providing bounds and detection prospects.

## Contribution

It introduces a comprehensive analysis combining $(g-2)_{}$ and dark matter data to constrain the 3-3-1 model's symmetry breaking scale and dark matter interactions.

## Key findings

- Favored symmetry breaking scale range identified
- Lower bounds on the scale established
- Predictions for fermion dark matter detection discussed

## Abstract

We find constraints on the highest scale of symmetry breaking of a model with gauge symmetry $SU(3)_C \otimes SU(3)_L \otimes U(1)_X$ with heavy neutral leptons in the fermion triplets, calculating the anomalous magnetic moment of the muon and using results of the relic abundance of dark matter and experiments searching for its direct detection. In order to do this, we have calculated the one-loop contribution of new particles in the model to $(g-2)_{\mu}$, finding a favoured region for the scale at which $SU(3)_L$ is broken, and we have found lower bounds for this scale making a comparison of the predictions for the detection of a fermion dark matter candidate in the model in terms of simplified dark matter models, identifying the dominant portal for its interactions with standard model particles, and using constraints for the relic abundance and spin-independent scattering cross section of the fermion candidate with protons.