Non-Universal Flipped Trinification Models with Arbitrary $\beta$

TL;DR

This paper investigates non-universal flipped trinification models with arbitrary , analyzing anomaly cancellation, proposing new family configurations, and deriving LHC bounds on the Z' boson mass for specific parameter choices.

Contribution

It introduces four new families of leptons and quarks within a unified gauge framework and identifies multiple anomaly-free models with realistic features.

Findings

Eight non-universal anomaly-free three-family models identified

Four non-universal two-family anomaly-free sets found

LHC bounds on Z' mass depend strongly on the mixing parameter  and  = -1/

Abstract

We explore the recently proposed gauge symmetry \( SU(3)_C \otimes SU(3)_L \otimes SU(3)_R \otimes U(1)_X \), which naturally embeds both the Left-Right symmetric model and the 3-3-1 model as subgroups. Within this unified framework, we propose four families of leptons and quarks. A detailed analysis of their contributions to gauge anomaly cancellation is carried out for a general value of the parameter $\beta$. From this analysis, eight non-universal anomaly-free three-family models and four non-universal two-family anomaly free sets were identified. The three-family models offer realistic extensions of the Standard Model, retaining several appealing features of the 3-3-1 models, while the two-family sets provide flexibility for constructing models with even numbers of families. We also report LHC bounds on the $Z'$ mass for the particular case $\beta = -1/\sqrt{3}$, considering all possible combinations of lepton and quark families. These limits exhibit a strong dependence on the mixing parameter $\theta$, which enters the couplings of Standard Model fermions to the $Z'$ boson.