Predictions of $m_b{/m}_{\tau }$ and $m_t$ in 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–mirror-generation pair (the fourth and antifourth generations) enabling the extra fermions to have $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\times \mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_Y$-invariant masses. Because of the contribution of the extra generations, all three running gauge couplings of $\mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}_C\times \mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\times \mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_Y$ 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 $\mu {=M}_Z$ insensitive to their initial values at $\mu {=M}_{\mathrm{GUT}},$ (2) the model predicts $R_{b\tau }{(M}_Z)\equiv Y_b{/Y}_{\tau }{|}_{\mu {=M}_Z}\approx 1.8$, which is consistent with the experimental value provided we take the ratio of Yukawa couplings at the GUT scale to be $R_{b\tau }{(M}_{\mathrm{GUT}}{)=Y}_b{/Y}_{\tau }{|}_{\mu {=M}_{\mathrm{GUT}}}=1/3\mathrm{}$, and (3) the $t$ mass prediction comes out to be $m_t$≈180 GeV which is also consistent with experiment.