Tetrahedron of flavors: One Three to rule them all

TL;DR

This paper proposes a novel flavor model based on a tetrahedral structure, extending trinification symmetry to a semi-simple $SU(3)_V imes SU(3)_H$, with implications for dark sectors and quark-lepton relations.

Contribution

It introduces a new flavor model using a tetrahedron of flavors with semi-simple symmetry, unifying fermion families without superfluous replication and exploring dark sectors and quark-lepton correspondence.

Findings

Model exhibits bi-trinification with coupled trinification cycles.

Includes a built-in dark sector within the flavor structure.

Proposes a non-Pati-Salam quark/lepton pairing with unified Yukawa origin.

Abstract

Under the conception that the total number three of fermion families must have the one and the same gauge theoretical origin as all other threes which accompany the single family grand unifiable group structure, we trade the trinification $SU(3)$ symmetry building block for its semi-simple Vertical-Horizontal symmetric $SU(3)_V \otimes SU(3)_H$ extension. The anomaly free flavor-chiral fermion representation is then constructed, solely out of threes and without any superfluous replication, by treating each standard $V$-triplet (and anti triplet) as an $H$-singlet, and conversely, by letting each standard $V$-singlet transform as an $H$-triplet (or anti triplet). The model can be schematically described by a tetrahedron of flavors. In its bi-trinification phase, the model exhibits two coupled trinification cycles, sharing the same color group, and is furthermore accompanied by a built-in dark sector. In its isomorphic quartification phase, the model presents a novel non-Pati-Salam version of quark/lepton correspondence, where quarks are paired with anti-leptons to cancel horizontal anomalies, and all fermion masses stem from one and the same Yukawa source.