A to Z of Flavour with Pati-Salam

We propose an elegant theory of flavour based on A(4) x Z(5) family symmetry with Pati-Salam unification which provides an excellent description of quark and lepton masses, mixing and CP violation. The A(4) symmetry unifies the left-handed families and its vacuum alignment determines the columns of Yukawa matrices. The Z(5) 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 Y-u = Y-v and Y-d similar to Y-e. 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 theta(C) approximate to 1/4. In particular, for a discrete choice of Z(5) phases, it predicts maximal atmospheric mixing, theta(l)(23) = 45 degrees +/- 0.5 degrees and leptonic CP violating phase delta(l)= 260 degrees +/- 5 degrees. The reactor angle prediction is theta(l)(13) = 9 degrees +/- 0.5 degrees, while the solar angle is 34 degrees greater than or similar to theta(l)(12) greater than or similar to 31 degrees, for a lightest neutrino mass in the range 0 less than or similar to m(1) less than or similar to 0.5 meV, corresponding to a normal neutrino mass hierarchy and a very small rate for neutrinoless double beta decay.