• neutrinos
• leptons
• mixing
• modular
• symmetry
• flavour
• eft
• hep
• susy
• Majorana

As we are entering the precision era of lepton mixing, many questions still remain unanswered: what is the nature of neutrino masses? Is there CP-violation in the lepton sector? How can we understand the hierarchy of charged-lepton masses?

In the recent past, a substantial effort went into the understanding of lepton mixing and masses through flavour symmetries. The goal of model-builders is to explain at once both the charged-lepton mass hierarchy and the neutrino sector (mixing and masses). In 2017 a new promising direction was suggested, consisting in a “bottom-up” approach based on Modular symmetry, where the Yukawa couplings of the Standard Model become modular forms of level N in the framework of Supersymmetry. For N ≤ 5 the modular group is isomorphic to the non-Abelian permutation groups S3, A4, S4 and A5, already employed in the context of discrete flavour symmetries. This approach has received considerable attention in the last few years, and some viable models have been put forward. The most successful models in the literature currently employ the higher-order groups A4, S4, A5 or their double-covers, but it is still unclear how a definitive model could be singled out among them.

In this work we propose a model based on the modular group isomorphic to the smallest non-Abelian group S3, which is the group of the permutations of three objects, showing (for the first time in lepton modular literature) that it is possible to reproduce the lepton masses and mixing with this group in a minimalist construction. This construction provides testable predictions for future neutrino experiments, among others: the mass ordering and the CP violation phase.