A to Z of Flavour with Pati-Salam

TL;DR

This paper presents a unified flavour model based on $A_4 imes Z_5$ symmetry and Pati-Salam unification, accurately predicting quark and lepton masses, mixing angles, and CP violation, with specific testable predictions for neutrino parameters.

Contribution

It introduces a novel $A_4 imes Z_5$ family symmetry combined with Pati-Salam unification to comprehensively explain fermion masses and mixings, including CP violation, with specific predictive power.

Findings

Predicts maximal atmospheric neutrino mixing angle of 45°

Forecasts a reactor angle of approximately 9°

Provides a specific value for the leptonic CP phase around 260°

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, $\theta^l_{23}=45^\circ\pm 0.5^\circ$ and leptonic CP violating phase $\delta^l=260^\circ \pm 5^\circ$. The reactor angle prediction is $\theta^l_{13}=9^\circ\pm 0.5^\circ$, while the solar angle is $34^\circ \geq \theta^l_{12}\geq 31^\circ$, for a lightest neutrino mass in the range $0 \leq m_1 \leq 0.5$ meV, corresponding to a normal neutrino mass hierarchy and a very small rate for neutrinoless double beta decay.