Constraints on Flavor Neutrino Masses and sin^2(2theta_{12})>>sin^2(theta_{13}) in Neutrino Oscillations

Abstract

To realize the condition of sin^2(2theta_{12})>>sin^2(theta_{13}), we find constraints on flavor neutrino masses M_{ij} (ij=e,μ,τ): C1) c_{23}^2 M_{μμ} + s_{23}^2 M_{ττ} \approx 2 s_{23} c_{23}M_{μτ} + M_{ee} and/or C2) |c_{23}M_{eμ} -s_{23}M_{eτ}|>> |s_{23}M_{eμ} +c_{23}M_{eτ}|, where c_{23}=cos(theta_{23}) (s_{23}=sin(theta_{23})) and theta_{12}, theta_{13} and theta_{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,μ,τ). To make definite predictions on neutrino masses and mixings, especially on sin(theta_{13}), that enable us to trace C1) and C2), M is assumed to possess texture zeros or to be constrained by textures with M_{μμ}=M_{ττ} or M_{eτ}=\pm M_{eμ} which turn out to ensure the emergence of the maximal atmospheric neutrino mixing at sin(theta_{13})->0. It is found that C1) is used by textures such as M_{eμ}=0 or M_{eτ}=0 while C2) is used by textures such as M_{eτ}=\pm M_{eμ}.