SUPERSYMMETRIC GRAND UNIFIED THEORIES - 2-LOOP EVOLUTION OF GAUGE AND YUKAWA COUPLINGS

We make a numerical study of gauge and Yukawa unification in supersymmetric grand unified models and examine the quantitative implications of fermion mass Ansatze at the grand unified scale. Integrating the renormalization group equations with alpha1(M(Z)) and alpha2(M(Z)) as inputs, we find alpha3(M(Z)) congruent-to 0.111(0.122) for M(SUSY) = m(t) and alpha3(M(Z)) congruent-to 0.106(0.116) for M(SUSY) = 1 TeV at one-loop (two-loop) order. Including b and tau Yukawa couplings in the evolution, we find an upper limit of m(t) less than or similar to 200 GeV from Yukawa unification. For given m(t) less than or similar to 175 GeV, there are two solutions for beta: one with tan beta > m(t)/m(b), and one with sin beta congruent-to 0.78(m(t)/150 GeV). Taking a popular Ansatz for the mass matrices at the unified scale, we obtain a lower limit on the top-quark mass of m(t) greater than or similar to 150(115) GeV for alpha3(M(Z)) = 0.11(0.12) and an upper limit on the supersymmetry parameter tan beta less than or similar to 50 if alpha3(M(Z)) = 0.11. The evolution of the quark mixing matrix elements is also evaluated.