Origin of Constrained Maximal CP Violation in Flavor Symmetry

TL;DR

This paper introduces the concept of constrained maximal CP violation in neutrino flavor symmetry, deriving conditions under which maximal CP violation and mixing angles are naturally realized through residual symmetries.

Contribution

It provides a parametrization-independent framework for CMCPV and proves a theorem linking residual symmetries to observed neutrino mixing parameters.

Findings

CMCPV characterized by specific residual symmetries

Theorem connecting residual symmetries to maximal CP violation

Special cases include $ au$-reflection and O(3) subgroups

Abstract

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, $(|\delta |, \theta_{23}) =(\frac{\pi}{2}, \frac{\pi}{4})$ 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.