New limits on the SUSY Higgs boson mass

We present new upper limits on the light Higgs boson mass mh in supersymmetric models. We consider two gravity-mediated models (with and without universal scalar masses) and two gauge-mediated models (with a 5+5 or 10+10 messenger sector). We impose standard phenomenological constraints, as well as SU(5) Yukawa coupling unification. Requiring that the bottom and tau Yukawa couplings meet at the unification scale to within 15%, we find the upper limit mh<114 GeV in the universal supergravity model. This reverts to the usual upper bound of 130 GeV with a particular nonuniversality in the scalar spectrum. In the 5+5 gauge-mediated model we find mh<97 GeV for small tanβ and mh≃116 GeV for large tanβ, and in the 10+10 model we find mh<94 GeV. We discuss the implications for upcoming searches at LEP-II and the Tevatron.