Study of Neutrino Phenomenology and $0\nu \beta \beta$ Decay using Polyharmonic $Maa\beta$ Forms

In this study, we explore the application of the ${\mathrm{\Gamma }}_3$ modular group, which is isomorphic to the $A_4$ symmetric group in developing a model for neutrino mass. We realized a non-supersymmetric left-right asymmetric model incorporating modular symmetry, where the modular forms consist of both holomorphic and non-holomorphic components and the Yukawa couplings expressed through polyharmonic $Maa\beta$ forms. To effectively implement the extended see-saw process in this model, we introduce one fermion singlet for each generation. We compute the effective mass and the associated half-life of $0\nu \beta \beta$ by accounting for both standard and non-standard contributions. Additionally, our study investigates the non-unitary effects and CP-violation arising from non-unitarity in this context. The model predicts values for the sum of neutrino masses and neutrino oscillation parameters are constraints with experiments. Furthermore, it yields satisfactory results in calculating the effective mass and half-life of $0\nu \beta \beta$ decay. These findings highlight the possibility and benefit of employing modular symmetry in neutrino mass model construction.