Gauge-Yukawa-Finite Unified Theories and their Predictions

Gauge-Yukawa unified theories, and in particular those which are finite beyond the unification scale, have been extended to include a soft supersymmetry breaking (SSB) sector. In the case of the Finite Unified Theories a new solution to the condition of twoloop finiteness of the SSB parameters is found, which requires a sum rule for the relevant scalar masses. The sum rule permits violations of the universality of the scalar masses which is found to lead to phenomenological problems. The minimal supersymmetric SU(5) Gauge-Yukawa model and two Finite-Gauge-Yukawa models have been examined using the sum rule. The characteristic features of these models are: a) the old agreement of the top quark mass prediction persists using the new data, b) the lightest Higgs boson is predicted to be around 120 GeV, c) the s-spectrum starts above 200 GeV. ∗Supported partly by the mexican projects CONACYT 3275-PE, PAPIIT IN110296, by the EU projects FMBI-CT96-1212 and ERBFMRXCT960090, and by the Greek project PENED95/1170;1981.