Construction of a minimal HiggsSO(10)supersymmetric grand unified model

Abstract

A full account is given of the procedure used by the authors to construct an $\mathrm{SO}(10)$ supersymmetric grand unified model of the fermion mass matrices. Various features of the model which gives remarkably accurate results for the quark and lepton masses and mixings were presented earlier in separate publications. The construction of the matrices is first discussed in the framework of effective operators, from which one naturally obtains the maximal ${\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{-}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ mixing, while the small angle or maximal mixing solutions for the solar neutrinos depend upon the nature of the Majorana matrix. A set of Higgs and fermion superfields is then introduced from which the Higgs and Yukawa superpotentials uniquely give the structure of the mass matrices previously obtained. The right-handed Majorana matrix arises from one Higgs field coupling to several pairs of superheavy conjugate neutrino singlets. For the simple version considered, 10 input parameters accurately yield the 20 masses and mixings of the quarks and leptons, and the 3 masses of the right-handed neutrinos.