Unification of gauge, family, and flavor symmetries illustrated in gauged SU(12) models

TL;DR

This paper proposes extending the gauge group to SU(12) to unify gauge, family, and flavor symmetries, providing models that predict neutrino properties and mixing angles without relying on discrete flavor symmetries.

Contribution

It introduces explicit SU(12) models that unify symmetries and predict fermion masses and mixings with minimal fine-tuning, avoiding discrete flavor symmetries.

Findings

Models predict neutrino mass hierarchy and octant of atmospheric mixing angle.

Predictions include leptonic CP violation and Majorana phases.

Fits to known fermion masses and mixing angles support model validity.

Abstract

To explain quark and lepton masses and mixing angles, one has to extend the standard model, and the usual practice is to put the quarks and leptons into irreducible representations of discrete groups. We argue that discrete flavor symmetries (and their concomitant problems) can be avoided if we extend the gauge group. In the framework of SU(12) we give explicit examples of models having varying degrees of predictability obtained by scanning over groups and representations and identifying cases with operators contributing to mass and mixing matrices that need little fine- tuning of prefactors. Fitting with quark and lepton masses run to the GUT scale and known mixing angles allows us to make predictions for the neutrino masses and hierarchy, the octant of the atmospheric mixing angle, leptonic CP violation, Majorana phases, and the effective mass observed in neutrinoless double beta decay.