A non-standard CP transformation leading to maximal atmospheric neutrino mixing

Abstract

We discuss a neutrino mass matrix ${\mathcal{M}}_{\nu }$ originally found by Babu, Ma, and Valle (BMV) and show that this mass matrix can be characterized by a simple algebraic relation. From this relation it follows that atmospheric neutrino mixing is exactly maximal while at the same time an arbitrary mixing angle ${\theta }_{13}$ of the lepton mixing matrix $U$ is allowed and--in the usual phase convention--CP violation in mixing is maximal; moreover, neither the neutrino mass spectrum nor the solar mixing angle are restricted. We put forward a simple seesaw extension of the Standard Model where the family lepton numbers are softly broken by the Majorana mass terms of the right-handed neutrino singlets and the BMV mass matrix results from a non-standard $CP$ symmetry.

Comments: 13 pages, plain LaTeX, no figures; minor modifications, final version for Phys. Lett. B