Eur. Phys. J. C (2025) 85: 1316
https://doi.org/10.1140/epjc/s10052-025-15017-9

Regular Article - Theoretical Physics

Phenomenology of inverse seesaw using $S_3$ modular symmetry

¹ High Energy Physics Research Unit, Department of Physics, Chulalongkorn University, 10330, Bangkok, Thailand
² Khon Kaen Particle Physics and Cosmology Theory Group (KKPaCT), Department of Physics, Khon Kaen University, 123 Mitraphap Rd, 40002, Khon Kaen, Thailand
³ Theoretical High-Energy Physics and Astrophysics Research Unit (ThEPA), Department of Physics, Srinakharinwirot University, 114 Sukhumvit 23 Rd., Wattana, 10110, Bangkok, Thailand
⁴ Department of Physics, School of Advanced Sciences, Vellore Institute of Technology, Tiruvalam Rd, Katpadi, 632014, Vellore, Tamil Nadu, India

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Received: 3 July 2025
Accepted: 1 November 2025
Published online: 17 November 2025

Abstract

Describing neutrino masses using the inverse seesaw mechanism with discrete flavor symmetry imposed through modular forms provides a testable framework at TeV scales with fewer parameters. $S_3$, the smallest finite modular group—naturally requiring only two new sets of heavy neutrinos—offers a unique yet largely unexplored setting for constructing minimal neutrino mass models. In this work, we construct the minimal supersymmetric inverse seesaw model based on the modular $S_3$ flavor symmetry. In our model, the light neutrino mass matrix depends on 6 real parameters: the complex modulus, an overall scale for light neutrino mass, a real ratio and a complex ratio of Yukawa coupling. Thanks to its minimality, our model offers various definite predictions: the lightest neutrino is massless, the neutrino masses are inverted ordering, the sum of the three light neutrino masses (${\sum }_i{m}_i$) is 100 meV, the effective mass for the end point of the beta decay spectrum is 50 meV, the effective mass for neutrinoless double beta decay ($m_{\mathit{ee}}$) is in the range $38-58$ meV. In particular, the predicted values for ${\sum }_i{m}_i$ and $m_{\mathit{ee}}$ from our model are within reach of the next generation experiments. Our model also predicts radiative lepton flavor violating decays $\ell \to {\ell }^{\prime }\gamma$ which are compatible with experimental constraints.