A simplest modular S3 model for leptons

We present minimalist constructions for lepton masses and mixing based on flavour symmetry under the modular group ΓN of lowest level N = 2. As opposed to the only existing model of Γ2 ≅ S3 formulated in a SUSY framework, the only non-SM field is the modulus τ, and a generalised CP symmetry is implemented. Charged-leptons masses are reproduced through symmetry arguments, without requiring fine-tuning of the free parameters. As a result, all lepton observables (masses and mixing) are reproduced within 1σ experimental range using a minimum of nine free real parameters (including the real and imaginary parts of the modulus). A normal ordering for the neutrino masses is predicted. We also obtain predictions for the CP violating phases: the Dirac CP phase is predicted around 1.6π, the Majorana phases lie in narrow regions near ±π. The sum of neutrino masses is within the current bound at ∼ 0.09 eV. Furthermore, we provide predictions for the neutrinoless double beta decay and tritium decay effective masses, around 20 meV. Given the reduced number of free input parameters as compared to the existing literature on modular S3, this work renews interest for a unified predictive model of quark-lepton sectors based on Γ2 ≅ S3.