Constraints on flavor neutrino masses andsin22ϑ12≫sin2ϑ13in neutrino oscillations

To realize the condition of ${sin}^{2}2{\vartheta }_{12}\gg {sin}^2{\vartheta }_{13}$, we find constraints on flavor neutrino masses $M_{ij}$ ($ij=e,\mu ,\tau$): (C1) $c_{23}^2{M}_{\mu \mu }+s_{23}^2{M}_{\tau \tau }\approx 2s_{23}{c}_{23}{M}_{\mu \tau }+M_{ee}$ and/or (C2) $|c_{23}{M}_{e\mu }-s_{23}{M}_{e\tau }|\gg |s_{23}{M}_{e\mu }+c_{23}{M}_{e\tau }|$, where $c_{23}=\cos {\vartheta }_{23}$ ($s_{23}=\sin {\vartheta }_{23}$) and ${\vartheta }_{12}$, ${\vartheta }_{13}$, and ${\vartheta }_{23}$ are the mixing angles for three flavor neutrinos. The applicability of (C1) and (C2) is examined in models with one massless neutrino and two massive neutrinos suggested by $\det (M)=0$, where $M$ is a mass matrix constructed from $M_{ij}$ ($i,j=e,\mu ,\tau$). To make definite predictions on neutrino masses and mixings, especially on $\sin {\vartheta }_{13}$, that enable us to trace (C1) and (C2), $M$ is assumed to possess texture zeros or to be constrained by textures with $M_{\mu \mu }=M_{\tau \tau }$ or $M_{e\tau }=\pm M_{e\mu }$, which turn out to ensure the emergence of the maximal atmospheric neutrino mixing at $\sin {\vartheta }_{13}\to 0$. It is found that (C1) is used by textures such as $M_{e\mu }=0$ or $M_{e\tau }=0$, while (C2) is used by textures such as $M_{e\tau }=\pm M_{e\mu }$.