Neutrino masses and mixing in an axion model

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 $$S_3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>S</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:math> 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 $$S_3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>S</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:math> 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 $$g-2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> anomaly within this framework. Additionally, we explore the axion’s properties and its role as dark matter.