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 $τ$ to the fundamental domain and scanning the allowed parameter space. We identify regions consistent with current neutrino oscillation data at the $3σ$ 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.

Figures (5)

• Figure 1: Parameter space between Re($\tau$) and Im($\tau$) for the model preferring NO and IO in left and right panel, respectively. The colour regions represent the different $\chi^2$ values.
• Figure 2: Allowed parameter spaces among the oscillation parameters for normal ordering (NO, left panel) and inverted ordering (IO, right panel). The contour lines indicate the allowed regions from the DUNE experiment, while the green contours show the NuFIT constraints. The scattered points correspond to the parameter space permitted by the model.
• Figure 3: Allowed parameter spaces between $\sin^2 \theta_{23}$, $\Delta m^2_{31}$ and $\delta_{CP}$ by the Models preferring NO (in left panel) and IO (in right panel). The contour lines denote the allowed regions from the DUNE experiment. The green contours correspond to the parameter space from NuFIT, while the scattered points represent the region allowed by the model.
• Figure 4: Effective Majorana mass for neutrino $m_{\beta\beta}$ (right panel) and $m_\nu$ (left panel) as a function of lightest neutrino mass for NO and IO, allowed by the model.
• Figure 5: Sum of neutrino masses $\sum m_i$ as a function of lightest neutrino mass for NO and IO, allowed by the model.