A to Z of Flavour with Pati-Salam

We propose an elegant theory of flavour based on $A_4\times Z_5$ 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 $Y^u=Y^{\nu }$ and $Y^d\sim Y^e$. 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 ${\theta }_C\approx 1\mathrm{/}4$. In particular it predicts maximal atmospheric mixing, ${\theta }_{23}^l={45}^{\circ }\pm {0.5}^{\circ }$ and leptonic CP violating phase ${\delta }^l={260}^{\circ }\pm 5^{\circ }$. The reactor angle prediction is ${\theta }_{13}^l=9^{\circ }\pm {0.5}^{\circ }$, while the solar angle is $34^\circ \geq \theta^l_{12}\geq 31^\circ$,foralightestneutrinomassintherange$0 \leq m_1 \leq 0.5$ meV, corresponding to a normal neutrino mass hierarchy and a very small rate for neutrinoless double beta decay.