Testing Gauge-Yukawa-Unified Models By $M_t$

Gauge-Yukawa Unification (GYU) relates the gauge and Yukawa couplings, thereby going beyond the usual GUTs, and it is assumed that the GYU in the third fermion generation implies that its Yukawa couplings are of the same order as the unified gauge coupling at the GUT scale. We re-examine carefully the recent observation that the top-bottom mass hierarchy can be explained to a certain extent in supersymmetric GYU models. It is found that there are equiv-top-mass-lines in the boundary conditions of the Yukawa couplings so that two different GYU models on the same line can not be distinguished by the top mass $M_t$ alone. If they are on different lines, they could be distinguished by $M_t$ in principle, provided that the predicted $M_t$'s are well below the infrared value $M_t$ (IR). We find that the ratio $M_t ({\rm IR})/\sin\beta$ depends on $\tan\beta$ for large $\tan\beta$ and the lowest value of $M_t ({\rm IR})$ is $\sim 188$ GeV. We focus our attention on the existing $SU(5)$ GYU models which are obtained by requiring finiteness and reduction of couplings. They, respectively, predict $M_t= (183+\delta^{\rm MSSM} M_t\pm 5)$ GeV and $(181+\delta^{\rm MSSM} M_t\pm 3)$ GeV, where $\delta^{\rm MSSM} M_t$ stands for the MSSM threshold correction and is $\sim -2$ GeV for the case that all the MSSM superpartners have the same mass $M_{\rm SUSY}$ with $\mu_H/M_{\rm SUSY} <<1$.