Radiative Dirac Neutrino Masses from Modular $S_3$ Symmetry in an Axion Model

TL;DR

This paper introduces a unified axion model with a modular $S_3$ symmetry that explains neutrino masses, flavor structure, the strong CP problem, and dark matter, predicting a Dirac neutrino mass matrix with one massless neutrino and an observable axion-photon coupling.

Contribution

It proposes a novel KSVZ-type axion model incorporating modular $S_3$ symmetry that generates radiative Dirac neutrino masses and links multiple fundamental issues in particle physics.

Findings

Neutrino mass matrix of rank two with one massless neutrino.

Predicted axion-photon coupling within reach of upcoming experiments.

Constraints on neutrino mass sum for both hierarchies.

Abstract

We present a unified axion model framework that simultaneously addresses the origin of neutrino masses, leptonic flavor structure, the strong CP problem, and dark matter. The model is based on a global $U(1)_{\rm PQ}$ symmetry combined with a modular $S_3$ symmetry and is realized within a novel class of KSVZ-type axion model. Exotic colored fermions and scalars mediate radiative neutrino mass generation at the one loop-level. The PQ charge assignment forbids tree-level neutrino masses and leaves a residual $Z_3$ symmetry that ensures the Dirac nature of neutrinos. In the minimal realization, the neutrino mass matrix is of rank two, predicting one massless neutrino. Consequently, the sum of neutrino masses is constrained for both the normal and inverted hierarchies. We analyze the implications for charged lepton flavor violation and the lepton $g-2$. The axion emerging from this framework dynamically resolves the strong CP problem and accounts for the observed dark matter abundance. Notably, the predicted axion-photon coupling is within reach of upcoming experiments and consistent with existing astrophysical and cosmological bounds.