Probing the grand-unification-scale mass spectrum through precision measurements on the weak-scale parameters

We study the renormalization-group evolution of gauge coupling constants including mass threshold effects of both light and heavy particles, in the minimal supersymmetric SU(5) grand unified model assuming supersymmetry breaking at ≲1 TeV. We show that a certain combination of superheavy masses ${\mathit{M}}_{\mathit{V}}^2$ ${\mathit{M}}_{\mathrm{\Sigma }}$ is tightly constrained, while the mass of the color-triplet Higgs boson, ${\mathit{M}}_{\mathit{H}}$, can vary from 2×${10}^{13}$ to 2×${10}^{17}$ GeV. With a relatively heavy color-triplet mass (${\mathit{M}}_{\mathit{H}}$∼${10}^{17}$ GeV), the present nucleon-decay experiments still allow superparticles below 1 TeV. The importance of a precise measurement on ${\mathrm{\alpha }}_3$ is stressed.