Right unitarity triangles and tri-bimaximal mixing from discrete symmetries and unification

TL;DR

This paper introduces models combining discrete symmetries and unification to predict tri-bimaximal lepton mixing and a right-angled CKM unitarity triangle, with specific vacuum alignments explaining CP phases.

Contribution

It presents new models that unify discrete family symmetries with SUSY GUTs to explain mixing angles and CP phases, predicting right-angled unitarity triangles in quark and lepton sectors.

Findings

Predicts lepton mixing sum rule with CP phase near 0, 90, 180, or 270 degrees

Achieves right-angled unitarity triangles in quark and lepton sectors

Provides vacuum alignment mechanism for phase predictions

Abstract

We propose new classes of models which predict both tri-bimaximal lepton mixing and a right-angled Cabibbo-Kobayashi-Maskawa (CKM) unitarity triangle, alpha approximately 90 degrees. The ingredients of the models include a supersymmetric (SUSY) unified gauge group such as SU(5), a discrete family symmetry such as A4 or S4, a shaping symmetry including products of Z2 and Z4 groups as well as spontaneous CP violation. We show how the vacuum alignment in such models allows a simple explanation of alpha approximately 90 degrees by a combination of purely real or purely imaginary vacuum expectation values (vevs) of the flavons responsible for family symmetry breaking. This leads to quark mass matrices with 1-3 texture zeros that satisfy the phase sum rule and lepton mass matrices that satisfy the lepton mixing sum rule together with a new prediction that the leptonic CP violating oscillation phase is close to either 0, 90, 180, or 270 degrees depending on the model, with neutrino masses being purely real (no complex Majorana phases). This leads to the possibility of having right-angled unitarity triangles in both the quark and lepton sectors.