Fermi-LAT GeV excess and muon $g-2$ in a modular $A_4$ symmetry

TL;DR

This paper presents a modular $A_4$ symmetry model that simultaneously explains the Fermi-LAT gamma-ray excess and the muon $g-2$ anomaly, aligning dark matter interactions with muons without violating lepton flavor constraints.

Contribution

It introduces a novel modular $A_4$ symmetry framework that links dark matter annihilation to muons and accounts for muon $g-2$ and gamma-ray excesses simultaneously.

Findings

Model successfully explains Fermi-LAT gamma-ray excess.

Model accounts for muon $g-2$ anomaly.

Allowed parameter space consistent with observations.

Abstract

The recent measurement of muon anomalous magnetic dipole moment (muon $g-2$) suggests that there might exist new physics that dominantly interacts with muons. The observed gamma-ray excess from Fermi-LAT indicates that dark matter annihilates into a specific charged fermions. We propose a successful model simultaneously to explain the Fermi-LAT GeV gamma-ray excess and sizable muon $g-2$ with a modular $A_4$ symmetry. Due to nature of this symmetry, our DM only interacts with pairs of muon and we explain sizable muon $g-2$ without suffering from constraints of any lepton flavor violations. We numerically show our allowed spaces on each measurements of Fermi-LAT, relic density of DM and muon $g-2$, randomly scanning our input parameters.