Towards a complete theory of fermion masses and mixings with SO(3) family symmetry and 5d SO(10) unification

We construct a complete 4d model of fermion masses and mixings in the Pati-Salam SU(4)SU(2)LSU(2)R framework governed by an SO(3) gauged Family Symmetry. The relevant low energy effective Yukawa operators are constructed so that the SO(3) flavons enter at the simplest possible one-flavon level, with couplings enforced by an additional U(1) × Z2 symmetry. The simplicity of the flavon sector allows the messenger sector to be fully specified, allowing the ultraviolet completion of the model at the 4d renormalizable level. The model predicts approximate tri-bimaximal lepton mixing via the see-saw mechanism with sequential dominance, and vacuum alignment of flavons, with calculable deviations described by the neutrino sum rule. We perform a numerical analysis of the emerging charged fermion spectra and mixings. The 4d model is shown to result from a 5d orbifold GUT model based on SO(3) × SO(10), where small flavon vacuum expectation values (VEVs) originate from bulk volume suppression