Neutrino Mass Matrix Predicted from the Symmetric Texture

Within the framework of grand unified theories, we carry out a full analysis of the symmetric texture to determine if such a texture can reproduce bi-large neutrino mixings, which have recently been indicated by solar and atmospheric neutrino experiments. It is found that so far as we adopt a symmetric texture, the so-called Froggatt-Nielsen mechanism does not naturally reproduce two large mixing angles. We find that, in order to obtain such mixing angles, we need to adopt a zero texture. By assuming this zero texture under SO(10), we are able to express the neutrino masses and mixing angles in terms of up quark masses, m t,m c and m u with two adjustable parameters for the right-handed Majorana masses. We also obtain the prediction ∣Ū e3∣ ≤0.11.