Lepton masses and mixing in non-holomorphic modular $A_4$ with universal couplings

Abstract

We propose a non-holomorphic modular $A_4$ model under the assumption of universal couplings. In this framework, a charged lepton mass hierarchy is not created through parameter fine tuning or hierarchical Yukawa couplings, but instead is determined by the modulus $\tau$, with certain modular weight assignments of right handed charged leptons. The experimental charged lepton masses are reproduced with high precision for values of $\tau$ located near modular fixed points. In neutrino sector the couplings are imposed to be equal in magnitude with different relative phases. By fixing the modulus $\tau$ from charged lepton sector, we perform a comprehensive scan over the phase parameters and modular weight assignments of the right handed neutrinos. We find that viable solutions arise only for normal neutrino mass ordering and a unique right handed neutrino modular weight, $k_N=-1$. The model yields strong correlations among mixing angles, the effective neutrinoless double beta decay parameter $m_{ee}$, and the total neutrino mass $\sum m_i$. These results underscore the predictive quality of non-holomorphic modular symmetry with minimal parameter inputs and offer implications for neutrino experiments and cosmological observations that can be tested.