Implications of texture 4 zero lepton mass matrices forUe3

Lepton mass matrices similar to texture 4 zero quark mass matrices, known to be quite successful in explaining the Cabibbo-Kobayashi-Maskawa (CKM) phenomenology, are considered for finding the mixing matrix element $U_{e3\mathrm{}}\left(\equiv s_{13}\right)$ respecting the CHOOZ constraint, with $s_{12}$ and $\Delta m_{12}^2$ constrained by the solar neutrino problem (SNP) and $s_{23}$ and $\Delta m_{23}^2$ constrained by the atmospheric neutrino problem (ANP). Taking the charged lepton mass matrix $M_l$ to be diagonal, we find that the ranges of $s_{13}$ corresponding to different SNP solutions very well include the corresponding values of $s_{13}$ found by Akhmedov et al. by considering a neutrino mass matrix $M_{\nu }$ with no texture zeros. Considering both $M_l$ and $M_{\nu }$ to be real and nondiagonal, the $s_{13}$ ranges for the four SNP solutions come out to be $\sim 0–0.19$ (large mixing angle), 0.038–0.093 (small mixing angle), 0.042–0.095 (low mass), and 0.038–0.096 (vacuum oscillation), which remain of the same order when $M_l$ and $M_{\nu }$ are considered to be complex and nondiagonal.