Majorana CP Violation in Approximately \mu-\tau Symmetric Models with det(M_\nu)=0

TL;DR

This paper investigates Majorana CP violation effects in neutrino mass models with zero determinant, focusing on approximate mu-tau symmetry, and classifies models based on their mixing angles and hierarchy types.

Contribution

It provides a model-independent analysis of Majorana CP violation in u neutrino mass matrices with zero determinant under mu-tau symmetry, classifying models into two categories with distinct phenomenological features.

Findings

Large Majorana phases possible in normal hierarchy

Inverted hierarchy with m1 ≈ -m2 shows large phases in (C1)

Phases are generally small in inverted hierarchy with m1 ≈ m2

Abstract

We discuss effects of Majorana CP violation in a model-independent way for a given phase structure of flavor neutrino masses. To be more predictive, we confine ourselves to models with $\det(M_\nu)=0$, where $M_\nu$ is a flavor neutrino mass matrix, and to be consistent with observed results of the neutrino oscillation, the models are subject to an approximate $\mu$-$\tau$ symmetry. There are two categories of approximately $\mu$-$\tau$ symmetric models classified as (C1) yielding $\sin^22\theta_{23} \approx 1$ and $\sin^2\theta_{13} \ll 1$ and (C2) yielding $\sin^22\theta_{23} \approx 1$ and $\Delta m_\odot^2/|\Delta m_{atm}^2|\ll 1$, where $\theta_{23(13)}$ stands for the mixing of massive neutrinos $\nu_2$ and $\nu_3$ ($\nu_1$ and $\nu_3$) and $\Delta m_ \odot ^2$ ($\Delta m_{atm}^2$) stands for the mass squared difference for atmospheric (solar) neutrinos. The Majorana phase can be large for the normal mass hierarchy and for the inverted mass hierarchy with $m_1\approx -m_2$ only realized in (C1) while they are generically small for the inverted mass hierarchy with $m_1\approx m_2$ in both (C1) and (C2). These results do not depend on a specific choice of phases in $M_\nu$ but hold true in any models with $\det(M_\nu)=0$ because of the rephasing invariance.