331 Models and Grand Unification: From Minimal SU(5) to Minimal SU(6)

TL;DR

This paper explores embedding the 331 model into SU(6) grand unification, proposing novel mechanisms for gauge coupling unification and neutrino mass origin, with potential implications for TeV-scale physics.

Contribution

It introduces a minimal SU(6) grand unification framework for the 331 model, allowing different multiplet multiplicities and neutrino mass generation without bulk exotics.

Findings

SU(3)_c d7 SU(3)_L d7 U(1)_X can be embedded in SU(6)

New gauge coupling unification pathways are proposed

TeV-scale 331 models with seesaw neutrino masses are feasible

Abstract

We consider the possibility of grand unification of the $\mathrm{ SU(3)_c \otimes SU(3)_L \otimes U(1)_X}$ model in an SU(6) gauge unification group. Two possibilities arise. Unlike other conventional grand unified theories, in SU(6) one can embed the $\mathrm{ SU(3)_c \otimes SU(3)_L \otimes U(1)_X}$ model as a subgroup such that different multiplets appear with different multiplicities. Such a scenario may emerge from the flux breaking of the unified group in an E(6) F-theory GUT. This provides new ways of achieving gauge coupling unification in $\mathrm{ SU(3)_c \otimes SU(3)_L \otimes U(1)_X}$ models while providing the radiative origin of neutrino masses. Alternatively, a sequential variant of the $\mathrm{ SU(3)_c \otimes SU(3)_L \otimes U(1)_X}$ model can fit within a minimal SU(6) grand unification, which in turn can be a natural E(6) subgroup. This minimal SU(6) embedding does not require any bulk exotics to account for the chiral families while allowing for a TeV scale $\mathrm{ SU(3)_c \otimes SU(3)_L \otimes U(1)_X}$ model with seesaw-type neutrino masses.