Two-loop calculations ofMbMτand heavy-fermion masses in the SU(5) model

Two-loop calculations of $\frac{M_b}{M_{\tau }}$ and $M_s$ in the SU(5) model for 3-5 generations are presented, based on the complete SU(3)×SU(2)×U(1) two-loop Higgs-Yukawa $\beta$ function. We find that the observed $\frac{M_b}{M_{\tau }}$ is consistent with three and four generations, in contrast to earlier work, but probably not with five. However if ${\Lambda }_{\overline{\mathrm{MS}}}$ is large (where $\overline{\mathrm{MS}}$ refers to the modified minimal-subtraction scheme), as may be required to explain the nonobservation of proton decay, the predicted $M_b$ may be inconsistent with experiment even for three generations. We find upper limits on the top-quark mass from the requirement that $\frac{M_b}{M_{\tau }}$ not be too large. We redo earlier calculations of $M_X$ and ${{sin}^2\theta }_W$, assuming the existence of heavy fermions, and essentially are in agreement with them. Lastly we consider the possibility of predicting the masses of heavy fermions by means of "pseudofixed points" of the Higgs-Yukawa renormalization-group equations.