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 thePati-Salam SU(4) x SU(2)_L x SU(2)_R framework governed by an SO(3) gaugedFamily Symmetry. The relevant low energy effective Yukawa operators areconstructed so that the SO(3) flavons enter at the simplest possible one-flavonlevel, with couplings enforced by an additional U(1) x Z_2 symmetry. Thesimplicity of the flavon sector allows the messenger sector to be fullyspecified, allowing the ultraviolet completion of the model at the 4drenormalizable level. The model predicts approximate tri-bimaximal leptonmixing via the see-saw mechanism with sequential dominance, and vacuumalignment of flavons, with calculable deviations described by the neutrino sumrule. We perform a numerical analysis of the emerging charged fermion spectraand mixings. The 4d model is shown to result from a 5d orbifold GUT model basedon SO(3) x SO(10), where small flavon vacuum expectation values originate frombulk volume suppression.Comment: 24 pages, 6 figures; typos corrected, minor comments & clarifications adde