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We construct a supersymmetric $SO(10) \times U(1)_F$ model of the Yukawainteractions at the grand unification scale from knowledge of aphenomenological set of mass matrices obtained by a previous bottom-upapproach. The $U(1)_F$ family symmetry determines the textures for the Majoranaand generic Dirac mass matrices, while the $SO(10)$ symmetry relates eachparticular element of the up, down, neutrino and charged lepton Dirac matrices.The dominant second and third family contributions in the Dirac sector arerenormalizable, while the remaining contributions to the Dirac mass matricesare of higher order, restricted by the $U(1)_F$ family symmetry to a small setof tree diagrams, and mainly complex-symmetric. The tree diagrams for theMajorana mass matrix are all non-renormalizable and of progressivelyhigher-order, leading to a nearly geometrical structure. Pairs of ${\bf 1, 45,10}$ and ${\bf 126}$ Higgs representations enter with those having large vacuumexpectation values breaking the symmetry down to $SU(3)_c \times SU(2)_L \timesU(1)_Y$ near the grand unification scale. In terms of 12 parameters expressedas the Yukawa couplings times vacuum expectation values for the Higgsrepresentations employed, a realistic set of 15 quark and lepton masses(including those for the 3 heavy righthanded Majorana neutrinos) and 8 mixingparameters emerges for the neutrino scenario involving the non-adiabaticconversion of solar neutrinos and the depletion of atmospheric muon-neutrinosthrough oscillations into tau-neutrinos.Comment: 32 pages, latex with style files attached, 1 figure in uuencoded  postscript fil

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Construction of an<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">SO</mml:mi><mml:mn /><mml:mo>(</mml:mo><mml:mn>10</mml:mn><mml:mo>)</mml:mo><mml:mn /><mml:mo>×</mml:mo><mml:mi mathvariant="normal">U</mml:mi><mml:mrow><mml:msub><mml:mrow><mml:mn /><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo><mml:mn /></mml:mrow><mml:mrow><mml:mi>F</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>model of the Yukawa interactions

Construction of anSO(10)×U(1)Fmodel of the Yukawa interactions