Families from Supergroups and Predictions for Leptonic CP Violation

TL;DR

This paper explores grand unified models based on supergroup decompositions, focusing on a specific SU(5) x SU(2) x U(1) model that predicts neutrino CP violation and fits lepton data.

Contribution

It introduces a new grand unified model using supergroup representations to naturally incorporate family symmetries and predicts leptonic CP violation.

Findings

Model fits lepton sector data

Predicts Dirac CP-violating phase in neutrinos

Provides explicit mass matrix structures

Abstract

As was shown in 1984 by Caneschi, Farrar, and Schwimmer, decomposing representations of the supergroup SU(M|N), can give interesting anomaly-free sets of fermion representations of SU(M) x SU(N) x U(1). It is shown here that such groups can be used to construct realistic grand unified models with non-abelian gauged family symmetries. A particularly simple three-family example based on SU(5) x SU(2) x U(1) is studied. The forms of the mass matrices, including that of the right-handed neutrinos, are determined in terms of SU(2) Clebsch coefficients; and the model is able to fit the lepton sector and predict the Dirac CP-violating phase of the neutrinos.. Models of this type would have a rich phenomenology if part of the family symmetry is broken near the electroweak scale.