Spontaneous breaking of SO(3) to finite family symmetries with supersymmetry — an A4 model

Abstract

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) × 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.