IMPLICATIONS OF YUKAWA UNIFICATION FOR THE HIGGS SECTOR IN SUPERSYMMETRIC GRAND-UNIFIED MODELS

The SU(5) unification-scale relation h(b) = h(tau) between the b-quark and tau-lepton Yukawa couplings severely constrains tan beta and the t-quark mass (even more so if h(t) = h(b) = h(tau) holds) in supersymm etric models. We examine the implications of these constraints for the Higgs sector assuming universal soft breaking terms, and emphasize th at both of these relations impose unique characteristics in terms of s ymmetries and of the spectrum. We further study the tan beta almost-eq ual-to 1 scenario, which is suggested by h(b) = h(tau), and, in partic ular, the loop-induced mass of the light Higgs boson. We compare the e ffective potential and renormalization group methods and stress the tw o-loop ambiguities in the calculation of the mass. These and a large e nhancement to the loop correction due to t-scalar left-right mixing co nsiderably weaken the upper bound on the mass of the light Higgs boson that has been reported. Nevertheless, we find that for this scenario the Higgs boson is probably lighter than 110 GeV, and typically lighte r than 100 GeV. Thus, it is in the mass range that may be relevant for the CERN Large Electron-Positron Collider (LEP II). Our numerical res ults are presented in a self-contained manner. We also discuss the glo bal symmetries of the Higgs potential, the issue of false (color-break ing) vacua, which may be important for tan beta almost-equal-to 1, two -loop calculations, and the effect of an additional Higgs singlet. We show that the approximate constraints that are often used to eliminate color-breaking vacua are not always relevant.