Majorana CP Violation in Approximately \mu-\tau Symmetric Models with det(M_\nu)=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 $\det(M_\nu)=0$, 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.Comment: 28 pages, 7 Figures, typos in equations and references corrected, version to appear in Prog. Theor. Phys. 123, No. 4 (2010, April

Dynamically Favored Chiral Symmetry Breakings in Supersymmetric Quantum Chromodynamics

By the use of an effective superpotential in supersymmetric quantum chromodynamics (SQCD) with N_f flavors and N_c colors of quarks for N_f>=N_c+2, the influence of soft supersymmetry (SUSY) breakings is examined to clarify dynamics of chiral symmetry breakings near the SUSY limit. In case that SQCD triggers spontaneous chiral symmetry breakings, it is possible to show that our superpotential dynamically favors the successive formation of condensates, leaving either SU(N_f-N_c) or SU(N_f-N_c+1) unbroken as a chiral nonabelian symmetry.Comment: 7 pages by RevTeX (with a note added