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 Mt alone. If they are on different lines, they could be distinguished by Mt in principle, provided that the predicted Mt’s are well below the infrared value Mt (IR). We find that the ratio Mt(IR)/ sinβ depends on tan β for large tan β and the lowest value of Mt(IR) is ∼ 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 Mt = (183 + δ Mt ± 5) GeV and (181 + δMt ± 3) GeV, where δMt stands for the MSSM threshold correction and is ∼ −2 GeV for the case that all the MSSM superpartners have the same mass MSUSY with μH/MSUSY << 1. Partially supported by the Grants-in-Aid for Scientific Research from the Ministry of Education, Science and Culture (No. 40211213). Address after Jan. 1st, ’96: Instituto de F́ısica, UNAM, Apdo. Postal 20-364, México 01000 D.F., México. On leave of absence from the Institute of Theoretical Physics, Warsaw University, ul. Hoza 69, 00-681 Warsaw, Poland. Partially supported by the Polish Committee for Scientific Research. On leave of absence from Physics Department, National Technical University, GR-157 80 Zografou, Athens, Greece. Partially supported by C.E.C. projects, SC1-CT91-0729; CHRX-CT93-0319.