Abstract
We make a numerical study of guage and Yukawa unification in supersymmetric grand unified models and examine the quantitative implications of fermion mass [ital Ansa]$[ital iuml]---[ital tze] at the grand unified scale. Integrating the renormalization group equations with [alpha][sub 1]([ital M][sub [ital Z]]) and [alpha][sub 2]([ital M][sub [ital Z]]) as inputs, we find [alpha][sub 3]([ital M][sub [ital Z]])[congruent]0.111(0.122) for [ital M][sub SUSY]=[ital m][sub [ital t]] and [alpha][sub 3]([ital M][sub [ital Z]])[congruent]0.106(0.116) for [ital M][sub SUSY]=1 TeV at one-loop (two-loop) order. Including [ital b] and [tau] Yukawa couplings in the evolution, we find an upper limit of [ital m][sub [ital t]][approx lt]200 GeV from Yukawa unification. For given [ital m][sub [ital t]][approx lt]175 GeV, there are two solutions for [beta]: one with tan[beta][gt][ital m][sub [ital t]]/[ital m][sub [ital b]], and one with sin[beta][congruent]0.78([ital m][sub [ital t]]/150 GeV). Taking a popular [ital Ansatz] for the mass matrices at the unified scale, we obtain a lower limit on the top-quark mass of [ital m][sub [ital t]][approx gt]150(115) GeV for [alpha][sub 3]([ital M][sub [ital Z]])=0.11(0.12) and an upper limit on the supersymmetry parameter tan[beta][approx lt]50 if [alpha][sub 3]([ital M][sub [ital Z]])=0.11. The evolution of the quark mixing elements is also evaluated.