Type-III seesaw under A4 modular symmetry

We make an attempt to study neutrino phenomenology in the framework of type-III seesaw by considering A4 modular symmetry in the super-symmetric context. In addition, we have included local U(1)B-L symmetry which eventually helps us to avoid certain unwanted terms in the superpotential. Hitherto, the seesaw being type-III, it involves the fermion triplet superfields Σ, along with which, we have included a singlet weighton field ρ. In here, modular symmetry plays a crucial role by avoiding the usage of excess flavon (weighton) fields. Also, the Yukawa couplings acquire modular forms which are expressed in terms of Dedekind eta function η. However, for numerical analysis we use q expansion expressions of these couplings. Therefore, the model discussed here is triumphant enough to accommodate the observed neutrino oscillation data. Additionally, it also successfully explains leptogenesis.