Non-Holomorphic $A_4$ Modular Symmetry in Type-I Seesaw: Implications for Neutrino Masses and Leptogenesis

Abstract

We propose a minimal extension of the Standard Model with right-handed neutrinos, governed by a non-holomorphic $A_{4}$ modular flavor symmetry. Within this model framework, the light neutrino masses are generated via the popular type-I seesaw mechanism in which the structure of the Dirac neutrino Yukawa couplings is decided by nonholomorphic modular forms. Unlike conventional flavor models with ad hoc flavon fields, the structure of Dirac and Majorana mass matrices is entirely determined by a modulus parameter $\tau$. We construct the predictive mass matrices for charged leptons, Dirac neutrinos, and right-handed Majorana neutrinos and show the compatibility with neutrino oscillation data by an appropriate choice of input model parameters. We present numerical analysis of two sets of benchmark points explaining neutrino masses while generating the correct amount of baryon asymmetry via thermal leptogenesis. We estimate numerically the values of CP-asymmetry and examine the evolution of the lepton asymmetry by studying Boltzman equations by considering both strong and washout regimes with CP-asymmetry parameter in the range $|\varepsilon_{1}| \sim 10^{-4}$--$10^{-8}$. The model predicts an effective Majorana mass in the few meV range, below current experimental bounds but within reach of next-generation $0\nu\beta\beta$ searches. The key feature of non-holomorphic $A_4$ modular symmetry naturally accommodates non-zero neutrino masses and mixings, minimizes the Yukawa arbitrariness, and establishes a direct connection between high-scale leptogenesis with low-energy neutrino observable parameters, thereby the model provides a testable link between neutrino flavor physics and cosmology.