Majorana CP Violation in Approximately μ-τSymmetric Models with det(M_ν)=0

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 $\det(M_ν)=0$, where $M_ν$ is a flavor neutrino mass matrix, and to be consistent with observed results of the neutrino oscillation, the models are subject to an approximate $μ$-$τ$ symmetry. There are two categories of approximately $μ$-$τ$ symmetric models classified as (C1) yielding $\sin^22θ_{23} \approx 1$ and $\sin^2θ_{13} \ll 1$ and (C2) yielding $\sin^22θ_{23} \approx 1$ and $Δm_\odot^2/|Δm_{atm}^2|\ll 1$, where $θ_{23(13)}$ stands for the mixing of massive neutrinos $ν_2$ and $ν_3$ ($ν_1$ and $ν_3$) and $Δm_ \odot ^2$ ($Δm_{atm}^2$) 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 $M_ν$ but hold true in any models with $\det(M_ν)=0$ because of the rephasing invariance.

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