# Fundamentals of the 3-3-1 Model with Heavy Leptons

## TL;DR

This paper reviews the 3-3-1 model with heavy leptons, analyzing its variants, symmetries, and scalar sector, providing a comprehensive theoretical foundation for understanding its structure and potential phenomenology.

## Contribution

It offers a detailed analysis of the 3-3-1HL model variants, symmetry considerations, and a novel diagonalization method for the scalar sector, enhancing the theoretical understanding of this model.

## Key findings

- Identification of four variants based on the parameter β
- Discretization of the potential for certain β values due to symmetry
- A new diagonalization method for the scalar sector

## Abstract

The work is a brief review of the theory based on the $SU(3)_c \otimes SU(3)_L \otimes U(1)_X$ gauge group in the presence of Heavy Leptons. Recent analysis have established a set of four possible variants for the 3-3-1HL, whose content arises according to the so-denoted variable $\beta$. Since it has been argued about the presence of stable charged particles in this sort of models, we divide the different sectors of the Lagrangian between universal and specific vertices, and conclude that the omission of $\beta$-dependent terms in the potential may induce to a discrete symmetry for the versions defined by $|\beta|=\sqrt{3}$. In the context of $|\beta|=\frac{1}{\sqrt{3}}$, where the new degrees of freedom have the same standard electric charges, additional Yukawa interactions may create decay channels into the SM sector. Furthermore, we introduce a method of diagonalization by parts in the Scalar sector motivated by a general consequence of the Goldstone theorem. In summary, we develop the most complete set of terms allowed by the symmetry group and resolve their definitive pieces in order to justify the model description present in the literature.