Inverse Seesaw Model in Non-holomorphic Modular $A_4$ Flavor Symmetry

This paper investigates an inverse seesaw model of neutrino masses based on non-holomorphic modular $A_4$ symmetry, extending the framework of modular-invariant flavor models beyond the conventional holomorphic paradigm. After the general theoretical framework is established, three concrete model realizations distinguished by their $A_4$ representation assignments and modular weight configurations for the matter fields are analyzed. Focusing on these three specific realizations, a comprehensive analysis of neutrino phenomenology is performed. By constraining the modulus parameter $\tau$ to the fundamental domain and systematically scanning the parameter space, regions compatible with current neutrino oscillation data are identified. The numerical results provide predictions for currently unmeasured quantities, including the absolute neutrino mass scale, Dirac CP-violating phase, and Majorana phases. These predictions establish specific, testable signatures for upcoming neutrino experiments, particularly in neutrinoless double beta decay and precision oscillation measurements. The framework offers a well-defined target for future experimental verification or exclusion, while demonstrating the phenomenological viability of non-holomorphic modular symmetry approaches to flavor structure.