---
abstract: 'In the minimal seesaw model, we derive required constraints on Dirac neutrino masses inducing maximal CP violation in neutrino oscillations. If the maximal atmospheric neutrino mixing is further assumed, Dirac neutrino masses are uniquely determined to respect $\mu$-$\tau$ flavored CP symmetry for neutrinos.'
author:
- Teruyuki Kitabayashi
- Masaki Yasuè
date: 'May, 2016'
title: Maximal CP Violation in Minimal Seesaw Model
---

\[sec:1\]Introduction
=====================

Neutrino oscillations have been theoretically predicted [@PMNS] and experimentally observed as atmospheric, solar, accelerator and reactor neutrino oscillations for more than a decade [@atmospheric; @solarold; @solar; @reactor; @accelerator; @sin13]. Extensive analyses of the current experimental data on neutrino oscillations seem to suggest the presence of the Dirac CP violation in neutrino physics [@NuData]. The Dirac CP violation is described by the CP-violating Dirac phase $\delta_{CP}$, which turns out to lie in the $1\sigma$-region of $\delta_{CP}/\pi = 1.13-1.64$ for the normal mass hierarchy (NH) or of $\delta_{CP}/\pi = 1.07-1.67$ for the inverted mass hierarchy (IH) [@NuData1]. There is another type of CP violation called Majorana CP violation. The relevant CP-violating phases are the Dirac phase and the Majorana phase [@CPViolationOrg], which enter into the Pentecorvo-Maki-Nakagawa-Sakata mixing matrix $U_{PNMS}$ [@PMNS] that converts the mass eigenstates of 