Neutrino Masses and Mixing in an Axion Model

TL;DR

This paper introduces a new model combining axion physics, neutrino mass generation, and dark matter, utilizing modular symmetry to explain neutrino mixing and address the strong CP problem.

Contribution

It develops a novel framework extending PQ symmetry with modular $S_3$ symmetry, leading to distinctive Yukawa interactions and neutrino mass mechanisms.

Findings

Neutrino masses generated radiatively via colored mediators

Axion acts as dark matter and solves the strong CP problem

Distinct phenomenology for holomorphic and non-holomorphic Yukawa interactions

Abstract

We propose a novel framework that simultaneously addresses three critical issues: tiny neutrino masses and their mixing patterns, dark matter, and the strong CP problem. Our model extends the Peccei-Quinn (PQ) symmetry by incorporating modular $S_3$ symmetry, which plays a central role in explaining the observed neutrino mixing structure. The field content includes two vector-like colored fermions and three colored scalars as $S_3$ singlets, an isospin doublet inert scalar and a singlet PQ scalar, each assigned appropriate modular weights. We show that such an extension, together with a suitable assignment of modular weights to the fields, can lead to holomorphic modular forms of Yukawa interactions, which can be derived from a superpotential. Furthermore, we explore an extension of the model to include non-holomorphic Yukawa interactions in the non-supersymmetric framework and show that the results are distinct from the holomorphic case. Tiny neutrino masses are generated radiatively through colored mediators, while the KSVZ-type axion appears to dynamically resolve the strong CP problem. We investigate the phenomenology of lepton flavor violation and the muon $g-2$ anomaly within this framework. Additionally, we explore the axion's properties and its role as dark matter.