Top-quark-mass prediction from supersymmetric grand unified theories

Abstract

We consider a supersymmetric grand-unified-theory (GUT) framework motivated by SO(10) or ${\mathrm{E}}_{6}$ unification in which the parameter $tan\ensuremath{\beta}(\ensuremath{\equiv}\frac{{v}_{2}}{{v}_{1}})$ of the minimal supersymmetric standard model is constrained by the condition that the Yukawa couplings ${h}_{t}$, ${h}_{b}$, and ${h}_{\ensuremath{\tau}}$ are all equal at the GUT scale. With ${\ensuremath{\alpha}}_{s}({M}_{Z})=0.106\ifmmode\pm\else\textpm\fi{}0.006$, the estimate for the $b$-quark mass, which depends on $tan\ensuremath{\beta}$, lies in the "observed" range ${m}_{b}({m}_{b})=4.25\ifmmode\pm\else\textpm\fi{}0.10$ GeV, provided that the top-quark mass is ${142}_{\ensuremath{-}49}^{+26}$ GeV.