Deviation from $\hat{I}¼-\ddot{I}„$ Symmetry with New Approaches

Abstract

We propose two new predictive neutrino mass matrix textures that deviate from $\hat{I}¼$-$\ddot{I}„$ symmetry and explore their phenomenological implications. These textures are significant due to their predictive nature and the unique approach they introduce for breaking the $\hat{I}¼$-$\ddot{I}„$ symmetry. Both textures predict six physical parameters and impose sharp constraints on $\hat{I}{¸}_{23}$ and $\hat{I}´$, considering both normal and inverted neutrino mass orderings. In addition, we realize the textures in their exact form within the framework of the seesaw mechanism, based on the $SU(2{)}_L\times A_4\times Z_3$ symmetry group.