Neutrino phenomenology, W-mass anomaly, and muon (g-2) in a minimal type-III seesaw model using a T0 modular symmetry

In this study, we introduce a model to illustrate neutrino phenomenology by incorporating two right-handed fermion triplet superfields, i.e., & sigma;Rj, in the presence of the modular symmetry & UGamma;03 & SIME; A04, a double cover of the A4 modular symmetry. The motivation in utilizing double cover is that, so far, only even modular forms have been considered for constructing modular invariant models, but, in this case, it is possible to extend the modular invariance approach to general integral weight modular forms, i.e., the odd weight modular forms. Hence, this type of amalgamation between T0 modular symmetry and minimally extending the seesaw can correctly explain the neutrino phenomenology. Additionally, we accommodate the most recent measurement of the W-boson mass, published by the CDF-II Collaboration, and shed some light on the recent results of muon (g - 2). Finally, we discuss lepton flavor violation in order to establish a constraint on the mass of right-handed fermion.

Automated summary

In this study, a model incorporating two right-handed fermion triplet superfields is introduced to illustrate neutrino phenomenology. By utilizing a double cover of the A4 modular symmetry, the model extends the modular invariance approach to odd weight modular forms. The model correctly explains neutrino phenomenology and establishes constraints on the mass of the right-handed fermion.