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

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 ${\sin }^{2}2{\theta }_{23}\approx 1$ and ${\sin }^2{\theta }_{13}\ll 1$ and (C2) yielding ${\sin }^{2}2{\theta }_{23}\approx 1$ 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.

Comments: 28 pages, 7 Figures, typos in equations and references corrected, version to appear in Prog. Theor. Phys. 123, No. 4 (2010, April)