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 $\sin\theta_{12} = 1/\sqrt{3}$ and $\sin\theta_{23} = 1/\sqrt{2}$, 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.