Lepton Masses and Mixing from Modular $S_4$ Symmetry

TL;DR

This paper develops minimal models of lepton masses and mixing using broken modular $S_4$ symmetry, successfully fitting experimental data and predicting CP-violating phases without introducing flavons.

Contribution

It introduces a novel approach using modular $S_4$ symmetry with a single modulus to model lepton properties, avoiding flavons and fitting experimental data.

Findings

Successfully fits charged lepton and neutrino oscillation data

Predicts Dirac and Majorana CP violation phases

Constructs minimal models based on modular forms

Abstract

We study models of lepton masses and mixing based on broken modular invariance. We consider invariance under the finite modular group $\Gamma_4 \simeq S_4$ and focus on the minimal scenario where the expectation value of the modulus is the only source of symmetry breaking, such that no flavons need to be introduced. After constructing a basis for the lowest weight modular forms, we build two minimal models, one of which successfully accommodates charged lepton masses and neutrino oscillation data, while predicting the values of the Dirac and Majorana CPV phases.