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Two Categories of Approximately μ-τ Symmetric Neutrino Mass Textures

TOKAI-HEP/TH-0602 with Kenichi Fuki, published in Nucl. Phys. B 783 No.1-2 (2007) 31-56 (Received date: 8 August, 2006).

$We present ten phenomenologically viable neutrino mass textures, which are approximately $\mu$-$\tau$ symmetric: two for the normal mass hierarchy, three for the inverted mass hierarchy, and five for the quasi degenerate mass pattern. Each texture falls into two categories characterized by either $\sin\theta_{13}\rightarrow 0$ (referred to as C1)), or $\sin\theta_{12}\rightarrow 0$ (referred to as C2)) in the $\mu$-$\tau$ symmetric limit, where $\theta_{12}$ and $\theta_{13}$, respectively stand for the $\nu_e$-$\nu_\mu$ and $\nu_e$-$\nu_\tau$ mixing angles. Our textures that depend on the signs of neutrino masses as well as on C1) and C2) are so constructed to satisfy general relations, which ensure that $\Delta m^2_\odot/\Delta m^2_{atm}(\equiv R)\ll 1$ and $\sin^2\theta_{13}\ll 1$, where $\Delta m^2_\odot$, and $\Delta m^2_{atm}$ are neutrino mass differences squared, respectively, for solar and atmospheric neutrinos. Three textures are found to provide $R\sim \sin^2\theta_{13}$.$

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