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Majorana CP Violation and mu-tau Synmmetry

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Majorana CP Violation in Approximately μ-τ Symmetric Models with det(Mν)=0

Share.gif (14997 ???)arXiv:1003.1438

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 $\Delta m_\odot^2/\vert\Delta m_{atm}^2\vert\ll 1$, 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 forthe 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.


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