Origin of constrained maximal CP violation in flavor symmetry

Current data from neutrino oscillation experiments are in good agreement with δ=−π2 and θ23=π4 under the standard parametrization of the mixing matrix. We define the notion of “constrained maximal CP violation” (CMCPV) for predicting these features and study their origin in flavor symmetry. We derive the parametrization-independent solution of CMCPV and give a set of equivalent definitions for it. We further present a theorem on how the CMCPV can be realized. This theorem takes the advantage of residual symmetries in neutrino and charged lepton mass matrices, and states that, up to a few minor exceptions, (|δ|,θ23)=(π2,π4) is generated when those symmetries are real. The often considered μ–τμ–τ reflection symmetry, as well as specific discrete subgroups of O(3), is a special case of our theorem.