Yukawa Coupling Thresholds: Application to the MSSM and the Minimal Supersymmetric SU(5) GUT

We consider a particular class of threshold corrections to Yukawa couplings and mass relations in the MSSM and supersymmetric grand unified models. We give a complete treatment of Yukawa coupling thresholds at the unification scale $\Mx$ and the effective supersymmetry scale $\Ms$ and apply them to corrections to the tree-level prediction $y_b(\Mx) = y_{\tau}(\Mx)$ in minimal supersymmetric SU(5). We apply both gauge and Yukawa coupling thresholds to gauge unification and the above Yukawa unification condition to find predictions for the top quark mass, $M_t$, the superheavy vector boson mass $\Mv$ and the colored Higgs triplet mass $\Mhs$. We discuss the dependencies of $\Mx$ and $\Mhs$ on $\alpha_s(M_Z)$, $M_t$ and the sparticle spectrum as well as those of $M_t$ on $\tan\beta$, $\alpha_s(M_Z)$ and the bottom quark mass, $M_b$. The effect of the Yukawa coupling thresholds on $M_t$ are given for representative sparticle spectra. We describe the quantitative differences between these effects for low and high $\tan\beta$. We also give new bounds on superheavy masses, incorporating proton decay as well as unification constraints, the former leading to a lower bound on $\alpha_s$.