Neutrino Textures from Modular $A_4$ Left--Right Symmetry: Experimental Signatures at DUNE and T2HK in the Post-JUNO Era

TL;DR

The paper develops seven two-zero neutrino textures within a left–right symmetric model using the modular group $Γ_{3}\cong A_{4}$ and an extended Type-II seesaw, introducing sterile fermions per generation. It computes the resulting $m_{\nu}$ patterns, effective Majorana masses, and LFV rates, and assesses experimental sensitivity at DUNE and T2HK, incorporating JUNO-like precision on $\theta_{12}$ and $\theta_{13}$. Through a $\chi^{2}$ analysis with GLoBES, the authors show that DUNE alone constrains the $(\theta_{23},\delta_{CP})$ plane for several textures, while the DUNE+T2HK combination with external priors yields highly predictive, compact islands, particularly for IH in textures $B_{2}$ and $B_{4}$. The results demonstrate that long-baseline experiments, aided by precise solar angle measurements, can robustly test and potentially falsify modular $A_{4}$ texture predictions, with significant implications for neutrino mass models and flavor symmetry. $m_{\text{eff}}$ lies well below current neutrinoless double beta decay bounds for most textures, and all seven textures respect current LFV limits, highlighting the model's consistency with present data and its strong predictive power for future experiments.

Abstract

We have realized different two-zero textures within the framework of the left right symmetric model using the $Γ_{3}\cong A_{4}$ modular group. The matter multiplets of the model are assigned as three singlet representations of the $A_{4}$ group, and their charge assignments together with the modular weights of the Yukawa couplings are chosen in such a way that different two-zero textures of the neutrino mass matrix are obtained. In total, we have successfully realized seven different two-zero textures. Furthermore, we have studied neutrinoless double beta decay and lepton flavor violating (LFV) processes, and have calculated the effective Majorana mass and the branching ratios for LFV processes for each of the textures. We further probe these two-zero textures at the long-baseline neutrino experiments DUNE and T2HK. We find that DUNE, especially when combined with T2HK, can significantly restrict the $θ_{23}-δ_{\rm CP}$ parameter space predicted by these textures. Moreover, the inclusion of high-precision determinations of $θ_{12}$ (from JUNO) and $θ_{13}$ leads to a substantial, further reduction of the allowed parameter space. For assumed inverted mass ordering, the synergy of DUNE and T2HK leads to a highly predictive scenario for the $B_{2}$ and $B_{4}$ textures, as the allowed regions collapse into tiny islands near the CP-conserving points in the lower and higher octant of $θ_{23}$, respectively.

Figures (10)

• Figure 1: 3$\sigma$ allowed regions in the $\theta_{23}$--$\delta_{\rm CP}$ plane for two-zero textures predicted by the modular $A_4$ left--right symmetric framework at DUNE in NH mode. The light blue band corresponds to the allowed region for different textures, while the light green (red) region shows the impact of including a prior on $\theta_{12}$ (both $\theta_{12}$ and $\theta_{13}$). The black line shows the globally allowed regions as per NuFit 6.0. when assumed hierarchy is normal.
• Figure 2: 3$\sigma$ allowed regions in the $\theta_{23}$--$\delta_{\rm CP}$ plane for two-zero textures predicted by the modular $A_4$ left--right symmetric framework at DUNE+T2HK in NH mode. The colour code is same as Figure. \ref{['fig:NH']}.
• Figure 3: 3$\sigma$ allowed regions in the $\theta_{23}$--$\delta_{\rm CP}$ plane for two-zero textures predicted by the modular $A_4$ left--right symmetric framework at DUNE (left) and DUNE+T2HK (right) when assumed mass ordering is normal. The colour code is same as Figure. \ref{['fig:NH']}.
• Figure 4: 3$\sigma$ allowed regions in the $\theta_{23}$--$\delta_{\rm CP}$ plane for two-zero textures predicted by the modular $A_4$ left--right symmetric framework at DUNE when assumed mass ordering is inverted. The colour code is same as Figure. \ref{['fig:NH']}.
• Figure 5: 3$\sigma$ allowed regions in the $\theta_{23}$--$\delta_{\rm CP}$ plane for two-zero textures predicted by the modular $A_4$ left--right symmetric framework at DUNE+T2HK when assumed mass ordering is inverted. The colour code is same as Figure. \ref{['fig:NH']}.