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We make a numerical study of gauge and Yukawa unification in supersymmetric grand unified models and examine the quantitative implications of fermion mass Ans\"atze at the grand unified scale. Integrating the renormalization group equations with ₁ (Mₙ) and ₂ (Mₙ) as inputs, we find ₃ (Mₙ) 0. 111 (0. 122) for Mₒₔₒₘ=mₓ and ₃ (Mₙ) 0. 106 (0. 116) for Mₒₔₒₘ=1 TeV at one-loop (two-loop) order. Including b and Yukawa couplings in the evolution, we find an upper limit of mₓ200 GeV from Yukawa unification. For given mₓ175 GeV, there are two solutions for: one with tan>mₓ{m₁}, and one with sin0. 78 (mₓ150 GeV). Taking a popular Ansatz for the mass matrices at the unified scale, we obtain a lower limit on the top-quark mass of mₓ150 (115) GeV for ₃ (Mₙ) =0. 11 (0. 12) and an upper limit on the supersymmetry parameter tan50 if ₃ (Mₙ) =0. 11. The evolution of the quark mixing matrix elements is also evaluated.
Barger et al. (Mon,) studied this question.
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