We study the SUSY SO(10) GUT with the symmetric two-zero textures of the quark/lepton mass matrix which realize the Georgi-Jarlskog relations in down-type quark and charged lepton masses. We show that the important constraints on such a framework come from the bottom-tau unification and the observed value of sin 2β, one of the angles in the CKM unitarity triangle. We investigate the symmetric two-zero textures assumed at the GUT scale by solving the MSSM renormalization group equations with right-handed neutrino threshold effects. Our results indicate that the value of tanβ is large and the representation of the Higgs field which couples to the third generation of left-and right-handed neutrinos is restricted by the bottom-tau unification condition. The textures with a vanishing 1-2 (and 2-1) element for up-type quarks and a vanishing 1-3 (and 3-1) element for down-type quarks are favored by the observed value of sin 2β.

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 |U

We study the symmetric texture of geometric form with 2-zeros to see if it is consistent with the presently-known neutrino masses and mixings. In the neutrino mass matrix elements we obtain numerically the allowed region of the parameters including CP violating phases, which can reproduce the present neutrino experiment data. The result of this analysis dictates the narrow region for the GUT model including Pati-Salam symmetry with texture zeros to be consistent with the experimental data. The |U e3 | and J CP are also predicted in such models. *

We study the symmetric 2-zero texture of the neutrino mass matrix, which is obtained from the symmetric Dirac neutrino mass matrix with 2 zeros and the right-handed Majorana neutrino mass matrix with general form via the seesaw mechanism, for the SUSY SO(10) GUT model including the Pati-Salam symmetry. We show that the only texture in our model, having a degenerate mass spectrum for the 1st and 2nd generation of the right-handed Majorana neutrino, can simultaneously account for the current neutrino experimental data, lepton flavor violating processes and the baryon asymmetry of the universe. Within such a framework, the predicted values of the light and heavy Majorana neutrino masses, together with |U e3 |, J CP and | M ee |, are almost uniquely determined. * ) Greiner used this configuration in the five-zero texture. Our model is different from their model with regard to this point. * ) The other possibility, that is, the effect of the deviation from m c in the 2-2 element of M u , is discussed in Appendix C.