Neutrino Textures from Modular $A_4$ Left--Right Symmetry: Experimental Signatures at DUNE and T2HK in the Post-JUNO Era
We have realized different two-zero textures within the framework of the left right symmetric model using the $\Gamma_{3}\cong A_{4}$ 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 $\theta_{23}-\delta_{\rm CP}$ parameter space predicted by these textures. Moreover, the inclusion of high-precision determinations of $\theta_{12}$ (from JUNO) and $\theta_{13}$ 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 $\theta_{23}$, respectively.