Twin Modular $S_4$ with $SU(5)$ GUT

TL;DR

This paper presents a novel $SU(5)$ GUT model with two modular $S_4$ symmetries that naturally explains fermion mass hierarchies and predicts specific lepton mixing patterns and neutrinoless double beta decay rates.

Contribution

It introduces a twin modular $S_4$ framework within $SU(5)$ GUT, utilizing weightons and residual symmetries to generate fermion hierarchies and mixing predictions.

Findings

Predicts TM$_1$ lepton mixing pattern.

Forecasts neutrinoless double beta decay rates near experimental sensitivity.

Explains fermion mass hierarchies via modular weights and residual symmetries.

Abstract

We discuss the $SU(5)$ grand unified extension of flavour models with multiple modular symmetries. The proposed model involves two modular $S_4$ groups, one acting in the charged fermion sector, associated with a modulus field value $\tau_T$ with residual $Z_3^T$ symmetry, and one acting in the right-handed neutrino sector, associated with another modulus field value $\tau_{SU}$ with residual $Z_2^{SU}$ symmetry. Quark and lepton mass hierarchies are naturally generated with the help of weightons, which are SM singlet fields, where their non-zero modular weights play the role of Froggatt-Nielsen charges. The model predicts TM$_1$ lepton mixing, and neutrinoless double beta decay at rates close to the sensitivity of current and future experiments, for both normal and inverted orderings, with suppressed corrections from charged lepton mixing due to the triangular form of its Yukawa matrix.