# A modular $A_4$ symmetric model of dark matter and neutrino

## TL;DR

This paper introduces a novel modular $A_4$ symmetric model that explains dark matter stability and neutrino masses, providing specific predictions for lepton mixing angles and identifying a unique dark matter candidate.

## Contribution

The model uniquely combines modular $A_4$ symmetry with dark matter and neutrino mass generation, offering specific phenomenological predictions and a distinctive dark matter candidate.

## Key findings

- Predicts narrow range for $ heta_{23}$ mixing angle: 0.56 to 0.624
- Identifies a single dark matter candidate distinguished by modular weight and mass hierarchy
- Provides a framework for discriminating this model from other $A_4$ modular symmetry models

## Abstract

We propose a model based on modular $A_4$ symmetry containing a dark matter candidate, realizing radiatively induced neutrino mass at one-loop level. One finds that stability of dark matter candidate can be assured by nonzero value of modular weight and heavy neutral fermion mass hierarchies, which include dark matter under the $A_4$ triplet, are uniquely determined; $M_X\ll M_2<M_3$. Therefore we clearly identify single dark matter field which can discriminate from the other models with $A_4$ modular symmetry. Then we discuss several phenomenological aspects and show predictions on the lepton sector.Especially, we find $0.56\lesssim\sin^2\theta_{23}\lesssim0.624$, which could have an advantage of this narrow region and be also discriminated from the other modular $A_4$ models.