# Common Origin of Non-zero $\theta_{13}$ and Dark Matter in an $S_4$ Flavour Symmetric Model with Inverse Seesaw

## TL;DR

This paper presents an $S_4$ flavor symmetric inverse seesaw model that simultaneously explains the non-zero reactor angle $ heta_{13}$ and dark matter relic abundance through one-loop corrections involving new particles, with implications for neutrinoless double beta decay.

## Contribution

It introduces a novel $S_4$ symmetric inverse seesaw model where one-loop corrections generate non-zero $ heta_{13}$ and account for dark matter, with the charged lepton correction case being more predictive.

## Key findings

- Non-zero $ heta_{13}$ generated at one loop level.
- Dark matter candidate identified as the lightest $Z^{Dark}_2$ odd particle.
- Inverted hierarchy disfavored by recent KamLAND-Zen data.

## Abstract

We study an inverse seesaw model of neutrino mass within the framework of $S_4$ flavour symmetry from the requirement of generating non-zero reactor mixing angle $\theta_{13}$ along with correct dark matter relic abundance. The leading order $S_4$ model gives rise to tri-bimaximal type leptonic mixing resulting in $\theta_{13}=0$. Non-zero $\theta_{13}$ is generated at one loop level by extending the model with additional scalar and fermion fields which take part in the loop correction. The particles going inside the loop are odd under an in-built $Z^{\text{Dark}}_2$ symmetry such that the lightest $Z^{\text{Dark}}_2$ odd particle can be a dark matter candidate. Correct neutrino and dark matter phenomenology can be achieved for such one loop corrections either to the light neutrino mass matrix or to the charged lepton mass matrix although the latter case is found to be more predictive. The predictions for neutrinoless double beta decay is also discussed and inverted hierarchy in the charged lepton correction case is found to be disfavoured by the latest KamLAND-Zen data.