Linear seesaw model with a modular $S_4$ flavor symmetry

TL;DR

This paper proposes a minimal linear seesaw model incorporating modular $S_4$ symmetry and gauged $U(1)_{B-L}$, predicting a normal neutrino mass hierarchy and a sum of neutrino masses around 60 meV.

Contribution

It introduces a novel minimal linear seesaw framework with modular $S_4$ symmetry and gauged $U(1)_{B-L}$, leading to specific neutrino mass predictions.

Findings

Neutrino mass matrix has rank two, resulting in one massless neutrino.

Model favors normal neutrino mass hierarchy.

Predicted sum of neutrino masses is approximately 60 meV.

Abstract

We discuss a linear seesaw model with as minimum field content as possible, introducing a modular $S_4$ with the help of gauged $U(1)_{B-L}$ symmetries. Due to rank two neutrino mass matrix, we have a vanishing neutrino mass eigenvalue, and only the normal mass hierarchy of neutrinos is favored through the modular $S_4$ symmetry. In our numerical $\Delta \chi^2$ analysis, we especially find rather sharp prediction on sum of neutrino masses to be around $60$ meV in addition to the other predictions.