Fermion masses and mixing in SO(10) GUT with a universal two-zero texture

TL;DR

This paper develops a SO(10) GUT model with a universal two-zero texture for fermion mass matrices, successfully fitting all known fermion masses and mixings and predicting neutrino properties and proton decay constraints.

Contribution

It introduces a novel application of the universal two-zero texture in SO(10) GUT, fitting all fermion data with minimal parameters and making testable predictions for neutrino and proton decay observables.

Findings

Model fits all fermion masses and mixing data very well.

Predicts leptonic CP-violating phase in (90°, 230°).

Provides ranges for right-handed neutrino masses and GUT parameters.

Abstract

We apply a universal two-zero texture (UTZT) to all mass matrices for matters in their flavour space in SO(10) GUT framework. This texture can be realised by assigning different charge for each family in a $Z_6$ symmetry. By fixing charged fermion masses at their best-fit values, we fit the rest 9 precisely measured observables (three angles and one CP-violating phase in the quark mixing, three angles in the lepton mixing, and two neutrino mass-squared differences) with seven model parameters. The model fits all data of fermion masses and mixing very well and the leptonic CP-violating phase is predicted in the range $(90^\circ, 230^\circ)$. The model further predicts the right-handed neutrino masses, with the lightest and heaviest of order $10^9$ and $10^{12}$ GeV, respectively. Gauge unification and proton decay have been checked with the assumption of a breaking chain with two intermediate symmetries above the electroweak scale. It indicates that $\alpha_{\rm GUT}$ ranges in (0.022,0.032) as long as the assumption of economical choice of Higgs contents, and $M_{\rm GUT}$ should be bigger than $4.5\times 10^{15}$ GeV to meet the Super-K bound. We show effective mass $m_{ee}$ for neutrinoless double beta decay, which provides us with a possibility to test grand unification with neutrinoless double beta decay experiments.