Ansatz of Leptonic Mixing: The Alliance of Bi-Maximal Mixing with a Single-Angle Rotation

Abstract: We introduce an ansatz of the PMNS matrix that consists of specific types of transformations. Bi-maximal mixing is taken for the neutrino masses, while a single-angle rotation in the 1-2 block is taken for the charged lepton masses. Motivated by the implications of the recent results on neutrino oscillations, $\theta_{23}$ in the first octant and non-zero $\theta_{13}$ are predicted by the ansatz. Three physical mixing angles are expressed in terms of a single variable, the 1-2 angle of charged leptons, so that a simple relation among the angles has been obtained: $\tan\theta_{13}=\sqrt{2}(\sin\theta_{23}-\sin\theta_{12})$. It follows that a model of the inverted hierarchy that can produce the given ansatz is proposed.