Abstract
We examine the problem of generating the observed fermion mass matrix in SO(10) grand unified theories from the general Yukawa couplings of two Higgs multiplets. We show that a 3\ifmmode\times\else\texttimes\fi{}3 matrix equation results, relating the observed lepton and up- and down-quark mass matrices to each other. The resulting overspecified system of three coupled nonlinear equations in two unknown functions of Higgs vacuum expectation values is shown to constrain the component mass and Kobayashi-Maskawa parameters. From the parameter constraints, we inspect typical solutions for allowed fermion mass matrices. In particular, we find the approximate quark-mass bounds of ${m}_{s}\ensuremath{\ge}300$ MeV and $19\ensuremath{\le}{m}_{t}\ensuremath{\le}38$ GeV, which are consistent with experimental estimates. Moreover, when coupled with a Gell-Mann\char22{}Ramond\char22{}Slansky mechanism for the generation of neutrino masses, information on the pattern of neutrino mixing can be gleaned.
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