Unifying left-right symmetry and 331 electroweak theories

TL;DR

This paper introduces a unified gauge theory combining left-right symmetry and 331 models, linking family number to color, and explaining neutrino masses via the seesaw mechanism.

Contribution

It presents a realistic gauge framework based on SU(3)_c x SU(3)_L x SU(3)_R x U(1)_X that naturally correlates family number with color and accommodates neutrino masses.

Findings

Family number equals the number of colors.

Neutrino masses arise from the canonical seesaw mechanism.

Different symmetry breaking paths lead to distinct extensions of the Standard Model.

Abstract

We propose a realistic theory based on the $\mathrm{SU(3)_c \otimes SU(3)_L \otimes SU(3)_R \otimes U(1)_{X}}$ gauge group which requires the number of families to match the number of colors. In the simplest realization neutrino masses arise from the canonical seesaw mechanism and their smallness correlates with the observed V-A nature of the weak force. Depending on the symmetry breaking path to the Standard Model one recovers either a left-right symmetric theory or one based on the $\mathrm{SU(3)_c \otimes SU(3)_L \otimes U(1)}$ symmetry as the "next" step towards new physics.