A model of quark and lepton mixing

We propose a model of quark and lepton mixing based on the tetrahedral A₄ family symmetry with quark-lepton unification via the tetra-colour Pati-Salam gauge group SU(4)_PS, together with SU(2)_L×U(1)_R. The "tetra-model" solves many of the flavour puzzles and remarkably gives ten predictions at leading order, including all six PMNS parameters. The Cabibbo angle is approximately given by θ_C≈1/4, due to the tetra-vacuum alignment (1,4,2), providing the Cabibbo connection between quark and lepton mixing. Higher order corrections are responsible for the smaller quark mixing angles and CP violation and provide corrections to the Cabibbo and lepton mixing angles and phases. The tetra-model involves an SO(10)-like pattern of Dirac and heavy right-handed neutrino masses, with the strong up-type quark mass hierarchy cancelling in the see-saw mechanism, leading to a normal hierarchy of neutrino masses with an atmospheric angle in the first octant, θ₂₃^l=40^∘±1^∘, a solar angle θ₁₂^l=34^∘±1^∘, a reactor angle θ₁₃^l=9.0^∘±0.5^∘, depending on the ratio of neutrino masses m₂/m₃, and a Dirac CP violating oscillation phase δ^l=260^∘±5^∘