Discrete family symmetry, Higgs mediators and θ 13

Abstract

We present a new (supersymmetric) framework for obtaining an excellent description of quark, charged lepton and neutrino masses and mixings from a Delta(6n^2) family symmetry with multiplet assignments consistent with an underlying SO(10) Grand Unification. It employs a Higgs mediator sector in place of the usual Froggatt-Nielsen messengers, with quark and lepton messengers, and provides significant improvements over existing models of this type having unsuppressed Yukawa couplings to the third generation and a simplified vacuum alignment mechanism. The neutrino mass differences are naturally less hierarchical than those of the quarks and charged leptons. Similarly the lepton mixing angles are much larger than those in the quark sector and have an approximate tri-bi-maximal (TB) mixing form for theta_{12} and theta_{23}. However the mixing angle theta_{13} is naturally much larger than in pure TB mixing and can be consistent with the value found in recent experiments. The magnitude of theta_{13} is correlated with a the predicted deviation of theta_{23} from bi-maximal mixing. The model has light familon fields that can significantly modify the associated SUSY phenomenology.