Solutions of the renormalization-group equations for minimal supergravity SU(5) grand unified theory and strong constraints on its parameters

A minimal N=1 supergravity SU(5) grand unified theory (GUT) is studied for a heavy top-quark mass (${\mathit{m}}_{\mathit{t}}$≥90 GeV). Renormalization-group equations are solved without neglecting the Yukawa couplings for the third generation of quarks and leptons. The solutions for mass parameters are expressed as linear combinations of the initial-value parameters of the model at the GUT scale and the coefficients are numerically obtained. This semianalytical expression of the solutions makes it easy to use the results for low-energy phenomenology. Approximate analytical solutions valid for small tanβ (${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{-}}$ collider LEP, the Collider Detector at Fermilab (CDF), and the proton decay experiments of Kamiokande, we can show that the very limited supersymmetric parameter space remains allowed.