Equal Majorana Phases from a Minimal and Predictive Neutrino Texture

We propose a new, minimal Majorana neutrino mass matrix texture and study its predictions within a partial tri-bimaximal (TBM) mixing scheme, where $\sin {\theta }_{12}=1\mathrm{/}\sqrt{3}$ and $\sin {\theta }_{23}=1\mathrm{/}\sqrt{2}$, with ${\theta }_{13}$ and $\delta$ treated as free parameters. The texture forbids ${\theta }_{13}=0$ and does not correspond to a $\mu -\tau$ symmetric structure. As a notable feature, the texture predicts the equality of the Majorana phases. In addition, we find that the predictions show distinct behavior depending on the sign of a single real texture parameter. The texture is realized through a hybrid framework of one Type-I seesaw and two Type-II seesaw mechanisms under an extended symmetry group, $SU(2{)}_L\otimes U(1{)}_Y\otimes A_4\otimes Z_{10}\otimes Z_7$ with properly chosen model parameters. The texture is seen to favor the normal hierarchy for neutrino masses.