Origin of Constrained Maximal CP Violation in Flavor Symmetry

Current data from neutrino oscillation experiments are in good agreement with $\delta =-\frac{\pi }{2}$ and ${\theta }_{23}^{}=\frac{\pi }{4}$. 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 advantage of residual symmetries in the neutrino and charged lepton mass matrices, and states that, up to a few minor exceptions, $(\mathrm{\mid }\delta \mathrm{\mid },{\theta }_{23})=(\frac{\pi }{2},\frac{\pi }{4})$ is generated when those symmetries are real. The often considered $\mu$-$\tau$ reflection symmetry, as well as specific discrete subgroups of O(3), are special cases of our theorem.