Top-quark and Higgs-boson mass bounds from a numerical study of supersymmetric grand unified theories

We run all the couplings of the minimal supersymmetric (SUSY) extension of the standard model, taking account of the Yukawa sector. After identifying the scale at which the gauge couplings unify, we place bounds on the top-quark mass by requiring equality of the bottom-quark and τ Yukawa couplings at that scale. For ${\mathit{M}}_{\mathrm{SUSY}}$=1 TeV, ${\mathit{M}}_{\mathit{b}}$=4.6 GeV, we find 139≤${\mathit{M}}_{\mathit{t}}$≤194 GeV, which remarkably satisfy the ρ-parameter bound. Furthermore, using the minimal SUSY boundary condition on the scalar quartic coupling, we obtain bounds for the mass of the Higgs boson, 44≤${\mathit{M}}_{\mathrm{Higgs}}$≤120 GeV.