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

TL;DR

This paper introduces a non-holomorphic modular $A_4$ symmetry-based linear seesaw model for neutrino masses, which is testable at DUNE and predicts observable neutrino properties within current experimental bounds.

Contribution

It develops a novel non-holomorphic modular $A_4$ framework for linear seesaw neutrino masses, reducing field content and providing testable predictions.

Findings

Consistent with current neutrino oscillation data at 3σ

Predicts neutrino mass scale and CP phases

Highlights testable signatures in future experiments

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.