A to Z of Flavour with Pati-Salam

Abstract

Abstract: We propose an elegant theory of flavour based on A4 × Z5 family symmetry with Pati-Salam unification which provides an excellent description of quark and lepton masses, mixing and CP violation. The A4 symmetry unifies the left-handed families and its vacuum alignment determines the columns of Yukawa matrices. The Z5 symmetry distinguishes the right-handed families and its breaking controls CP violation in both the quark and lepton sectors. The Pati-Salam symmetry relates the quark and lepton Yukawa matrices, with Yu = Yν and Yd ~ Ye. Using the see-saw mechanism with very hierarchical right-handed neutrinos and CSD4 vacuum alignment, the model predicts the entire PMNS mixing matrix and gives a Cabibbo angle θC ≈ 1/4. In particular, for a discrete choice of Z5 phases, it predicts maximal atmospheric mixing, θ23l = 45° ± 0.5° and leptonic CP violating phase δl = 260° ± 5°. The reactor angle prediction is θ13l = 9° ± 0.5°, while the solar angle is 34° ≳ θ12l ≳ 31°, for a lightest neutrino mass in the range 0 ≲ m1 ≲ 0.5 meV, corresponding to a normal neutrino mass hierarchy and a very small rate for neutrinoless double beta decay.