Spontaneous breaking of $SO(3)$ to finite family symmetries with supersymmetry - an $A_4$ model

TL;DR

This paper introduces a novel supersymmetric framework for breaking continuous $SO(3)$ symmetry into finite family symmetries like $A_4$, and constructs a lepton model consistent with observed mixing patterns.

Contribution

It presents the first supersymmetric potentials for breaking $SO(3)$ to finite groups and develops a viable $A_4$ lepton model from $SO(3)\times U(1)$ with phenomenological implications.

Findings

Successful breaking of $SO(3)$ to $A_4$, $Z_3$, and $Z_2$ using supersymmetric potentials.

A phenomenologically viable $A_4$ lepton model with realistic mixing and masses.

Resolution of domain wall problems in models with gauged $SO(3)$.

Abstract

We discuss the breaking of $SO(3)$ down to finite family symmetries such as $A_4$, $S_4$ and $A_5$ using supersymmetric potentials for the first time. We analyse in detail the case of supersymmetric $A_4$ and its finite subgroups $Z_3$ and $Z_2$. We then propose a supersymmetric $A_4$ model of leptons along these lines, originating from $SO(3)\times U(1)$, which leads to a phenomenologically acceptable pattern of lepton mixing and masses once subleading corrections are taken into account. We also discuss the phenomenological consequences of having a gauged $SO(3)$, leading to massive gauge bosons, and show that all domain wall problems are resolved in this model.