Fritzsch-Stech model in SO(10).

Abstract

The combined Fritzsch-Stech model for quarks is consistent with our present knowledge of quark masses and mixing angles. A possible way to extend it to leptons---by using an SO(10) framework---has been suggested by Bottino, Kim, Nishiura, and Sze. We investigate this model further and find some new features. It is first noted that the allowed quark masses are somewhat sensitive to the experimental uncertainties in the input parameters. This is carefully analyzed and we find that the original Stech Ansatz for the hadron sector is consistent. However, if the top-quark mass is greater than about 45 GeV, this Ansatz must be slightly modified. It is found that in a model of the present type the seesaw mechanism for neutrino masses may be drastically modified. This occurs because in SO(10) it is likely that the matrix of heavy ``right-handed'' neutrinos is close to a singular matrix. This feature is analyzed both analytically and numerically. Various patterns involving two extremely light neutrinos and one intermediate-mass (order of several MeV) neutrino which may arise are compared with experiment. More orthodox and perhaps more probable patterns for neutrino masses are also discussed. The lepton-mixing matrices are predicted and the results support recent explanations of the solar-neutrino paradox.