Fermion Masses and Mixing in Pati-Salam Unification with $S_3$ Modular Symmetry

TL;DR

This paper introduces the first implementation of $S_3$ modular symmetry in Pati-Salam unification to explain quark and lepton flavor structures, fitting experimental data and predicting neutrino properties.

Contribution

It presents three novel models integrating $S_3$ modular symmetry into Pati-Salam unification, successfully fitting flavor observables and making testable neutrino predictions.

Findings

All models favor normal neutrino mass ordering.

Models I and III predict $m_{etaeta}$ within reach of future experiments.

Predicted ranges for CP phases and neutrino masses enable experimental testing.

Abstract

Modular invariance has recently paved new promising directions in flavor model building. Motivated by this development, we present in this work the first implementation of the $S_3$ modular symmetry within the Pati-Salam unification framework, addressing the flavor structure of quarks and leptons. Assigning left- and right-handed matter fields as $S_3$ doublets or singlets, we propose three benchmark models that achieve compelling fits to sixteen observables including charged fermion mass ratios and flavor mixing parameters. Light neutrino masses arise via the type-I seesaw mechanism, and neutrino oscillation parameters are explored in light of the latest NuFIT-6.0 results. All models favor a normal neutrino mass ordering, with the atmospheric mixing angle lie in the lower octant. For models I and III, the effective Majorana mass $m_{\beta\beta}$ is within the reach of upcoming neutrinoless double-beta decay experiments, while it is too small to be detected in model II. Predicted leptonic CP-violating phases, the sum of active neutrino masses, and Majorana phases span wide but distinctive ranges, enabling future experiments to test and differentiate the proposed models.