A to Z of Flavour with Pati-Salam

Abstract

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 ${\theta }_C\approx 1/4$. 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 $34^{\circ }\ge {\theta }_{12}^l\ge 31^{\circ }$, for a lightest neutrino mass in the range $0\le m_1\le 0.5$ meV, corresponding to a normal neutrino mass hierarchy and a very small rate for neutrinoless double beta decay.

arXiv comment38 pages, 28 figures, published version

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