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Constraints on Flavor Neutrino Masses and sin212>>sin2θ13 in Neutrino Oscillations

  • TOKAI-HEP/TH-0501 with Ichiro Aizawa and Teruyuki Kitabayashi in Phys. Rev. D  71 No.7 (April, 2005) 075011 1-14 (Received date: February, 2005)..
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To realize the condition of \sin^22\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 2 s_{23} c_{23}M_{\mu\tau} + M_{ee} and/or C2) \vert c_{23}M_{e\mu} -s_{23}M_{e\tau}\vert \gg \vert s_{23}M_{e\mu} +c_{23}M_{e\tau}\vert, 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}\rightarrow 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}.

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