Neutrino masses and mixing in an axion model

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 S₃ 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 S₃ 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 $$g-2$$ g - 2 anomaly within this framework. Additionally, we explore the axion’s properties and its role as dark matter.