The Energy Criterion and Dynamical Symmetry Breaking in a $SU(3)_L \otimes U(1)_X$ Extension of the Standard Model

TL;DR

This paper explores the potential for dynamical symmetry breaking in certain $SU(3)_L imes U(1)_X$ extensions of the Standard Model, proposing an energy criterion to identify the most likely model version at TeV scales.

Contribution

It introduces an energy criterion to determine which $SU(3)_L imes U(1)_X$ model version is most likely realized in nature, focusing on dynamical symmetry breaking without fundamental scalars.

Findings

The energy criterion favors specific model versions at TeV scale.

Dynamical symmetry breaking can occur without fundamental scalars in these models.

The relation between coupling constants guides the symmetry breaking analysis.

Abstract

The coupling constants $g_L$ and $g_X$ of some versions of the $SU(3)_L\otimes U(1)_X$ extension of the standard model are related through to relationship $g^2_X/g^2_L= \sin^2\theta_W/(1 - 4\sin^2\theta_W)$. This fact suggest that the $SU(3)_L\otimes U(1)_X$ gauge symmetry in this class of models can be broken dynamically to the standard model at TeV scale without requiring the introduction of fundamental scalars. This possibility was investigated by Das and Jain who considered only the first version of this class of models. In this brief report we discuss an energy criterion to verify the most probable version of the $SU(3)_L\otimes U(1)_X$ model that is realized in nature.