Ansatz of leptonic mixing: The alliance of bi-maximal mixing with a single-angle rotation

Abstract

We introduce an ansatz of the Pontecorvo-Maki-Nakagawa-Sakata (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, θ23 in the first octant and non-zero θ13 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 θ13 = \(\sqrt 2 \)(sin θ23 − sin θ12). Finally a model of the inverted hierarchy that can produce the given ansatz is proposed.