Predictions ofmb/mτandmtin an asymptotically nonfree theory
We discuss an extension of the minimal supersymmetric standard model with five generations of matter superfields. The extra generations are assumed to form a generation{endash}mirror-generation pair (the fourth and antifourth generations) enabling the extra fermions to have SU(2){sub L}{times}U(1){sub Y}-invariant masses. Because of the contribution of the extra generations, all three running gauge couplings of SU(3){sub C}{times}SU(2){sub L}{times}U(1){sub Y} become asymptotically nonfree while preserving gauge coupling unification at the grand unified theory (GUT) scale. We show that, due to the asymptotically nonfree character of the gauge couplings, (1) the top and bottom Yukawa couplings are strongly focused onto infrared fixed points as they are evolved down in scale making their values at {mu}=M{sub Z} insensitive to their initial values at {mu}=M{sub GUT}, (2) the model predicts R{sub b{tau}}(M{sub Z}){equivalent_to}Y{sub b}/Y{sub {tau}}{vert_bar}{sub {mu}=M{sub Z}}{approx}1.8, which is consistent with the experimental value provided we take the ratio of Yukawa couplings at the GUT scale to be R{sub b{tau}}(M{sub GUT})=Y{sub b}/Y{sub {tau}}{vert_bar}{sub {mu}=M{sub GUT}}=1/3, and (3) the t mass prediction comes out to be m{sub t}{approx}180 GeV which is also consistent with experiment. {copyright} {ital 1997} {ital The American Physical Society}