Neutrino Masses and Higher Degree Siegel Modular Forms

Abstract

In this work, we have analyzed a neutrino model within the distinct framework of modular forms with degree, $ g>1 $ . This offers a more generalized scenario of modular forms which is popularly known as Siegel modular forms. We explore the implications of this special case of automorphic forms for physics beyond the standard model (BSM) within the lepton sector. In our model, we explicitly treat the Yukawa couplings as Siegel modular forms with both degree and level being equivalent to 2. We restrict our modulus parameter for $ \tau_{1}=\tau_{2} $ spanning within the finite modular $ S_{4}\times Z_{2} $ space. This helps us for a broader understanding of the multiplets at higher degree and simplifies the process of model building of the fermion masses. At the end, we compute the unknown neutrino oscillation parameters and find the optimal values of the modulus parameters $ \tau_{1} $ and $ \tau_{3} $ for which the values of the Yukawa couplings are consistent at $ 3\sigma $ for the input parameters of neutrinos as given in NuFIT 5.2 and discuss its underlying physics.