# On trilinear terms in the scalar potential of 3-3-1 gauge models

## TL;DR

This paper investigates the impact of trilinear scalar potential terms in 3-3-1 gauge models, revealing that the expected large cubic coupling must be much smaller than previously assumed to align with observed Higgs properties.

## Contribution

It demonstrates that the cubic term in the scalar potential must be significantly smaller than the symmetry-breaking scale, challenging prior assumptions in 3-3-1 models.

## Key findings

- The cubic coupling f must be much less than the symmetry-breaking scale w.
- Large cubic couplings f ≈ w are incompatible with the Higgs mass and eigenbasis analysis.
- Constraints on scalar potential terms affect model viability and parameter choices.

## Abstract

The trilinear terms {\normalsize of the form $\sqrt{2} f\epsilon^{ijk} \rho_i \chi_j\phi_k$} in the scalar potential of a 3-3-1 gauge model are considered. When looking for the eigenbasis of the massive physical Higgs bosons that survive the spontaneous symmetry breakdown of the model -- in light of the observed SM-like Higgs boson with mass $m_{h}\simeq125$ GeV reported in 2012 at the LHC -- one gets a strong constraint to the cubic term. It has to be smaller than usual $f\ll w$, in flagrant contradiction with the large one $f\simeq w$ which is propagated in the literature to date.