A Model of Fermion Masses and Flavor Mixings with Family Symmetry $SU(3)\otimes U(1)$

TL;DR

This paper proposes a family symmetry model with $SU(3)\otimes U(1)$ to explain fermion masses and mixings, successfully fitting current data and predicting key neutrino parameters for future tests.

Contribution

It introduces a novel $SU(3)\otimes U(1)$ family symmetry framework with discrete $Z_2$ to unify fermion mass and mixing explanations, including neutrino mass generation.

Findings

Accurately fits all current fermion mass and mixing data.

Predicts the first-generation quark masses.

Provides predictions for neutrino mixing angles and CP violation.

Abstract

The family symmetry $SU(3)\otimes U(1)$ is proposed to solve flavor problems about fermion masses and flavor mixings. It's breaking is implemented by some flavon fields at the high-energy scale. In addition a discrete group $Z_{2}$ is introduced to generate tiny neutrino masses, which is broken by a real singlet scalar field at the middle-energy scale. The low-energy effective theory is elegantly obtained after all of super-heavy fermions are integrated out and decoupling. All the fermion mass matrices are regularly characterized by four fundamental matrices and thirteen parameters. The model can perfectly fit and account for all the current experimental data about the fermion masses and flavor mixings, in particular, it finely predicts the first generation quark masses and the values of $\theta^{\,l}_{13}$ and $J_{CP}^{\,l}$ in neutrino physics. All of the results are promising to be tested in the future experiments.