An Explicit SO(10) x U(1)_F Model of the Yukawa Interactions

Abstract

We construct an explicit $SO(10) \times U(1)_F$ model of the Yukawa interactions by using as a guide previous phenomenological results obtained from a bottom-up approach to quark and lepton mass matrices. The global $U(1)_F$ family symmetry group sets the textures for the Majorana and generic Dirac mass matrices by restricting the type and number of Higgs diagrams which can contribute to each matrix element, while the $SO(10)$ group relates each particular element of the up, down, neutrino and charged lepton Dirac matrices. The Yukawa couplings and vacuum expectation values associated with pairs of {\bf 1,~45, 10,} and {\bf 126} Higgs representations successfully correlate all the quark and lepton masses and mixings in the scenario incorporating the nonadiabatic solar neutrino and atmospheric neutrino depletion effects.