# Trimaximal TM$_1$ mixing with two modular $S_4$ groups

## TL;DR

This paper proposes a minimal flavor model with twin modular symmetries involving two $S_4$ groups, predicting TM$_1$ lepton mixing and a new neutrino mass sum rule with implications for neutrino mass bounds.

## Contribution

It introduces a novel minimal flavor model with twin modular $S_4$ symmetries that predicts TM$_1$ mixing and derives a new neutrino mass sum rule.

## Key findings

- Predicts TM$_1$ lepton mixing pattern.
- Derives a neutrino mass sum rule.
- Imposes lower bounds on neutrino masses.

## Abstract

We discuss a minimal flavour model with twin modular symmetries, leading to trimaximal TM$_1$ lepton mixing in which the first column of the tri-bimaximal lepton mixing matrix is preserved. The model involves two modular $S_4$ groups, one acting in the neutrino sector, associated with a modulus field value $\tau_{SU}$ with residual $Z^{SU}_2$ symmetry, and one acting in the charged lepton sector, associated with a modulus field value $\tau_{T}$ with residual $Z^{T}_3$ symmetry. Apart from the predictions of TM$_1$ mixing, the model leads to a new neutrino mass sum rule which implies lower bounds on neutrino masses close to current limits from neutrinoless double beta decay experiments and cosmology.