A Predictive Non-Holomorphic Modular $A_4$ Linear Seesaw Framework Testable at DUNE

Abstract

We study a realization of neutrino masses within the linear seesaw mechanism based on non-holomorphic modular $A_4$ symmetry, extending modular-invariant flavor models beyond the conventional holomorphic framework. The model is constructed in a non-supersymmetric setting and involves six heavy $SU(2)_L$ singlet fermions, $N_R$ and $S_L$, together with a single flavon field, thereby significantly reducing the field content. The modular transformation properties of the Yukawa couplings under $A_4$ symmetry lead to a highly constrained neutrino mass matrix with a distinctive flavor structure. After presenting the general theoretical framework, we perform a systematic numerical analysis of neutrino phenomenology by restricting the modulus parameter $\tau$ to the fundamental domain and scanning the allowed parameter space. We identify regions consistent with current neutrino oscillation data at the $3\sigma$ level and obtain predictions for currently unknown observables, including the absolute neutrino mass scale and leptonic CP-violating phases. We further examine the implications for neutrinoless double beta decay, highlighting testable signatures in upcoming precision oscillation and rare-process experiments. These results demonstrate the phenomenological viability and predictive power of non-holomorphic modular symmetry in linear seesaw neutrino mass models.