Exact Finite and Gauge-Yukawa Unified Theories and Their Predictions

The recent developments in the soft supersymmetry breaking (SSB) sector of Gauge-Yukawa and Finite Unified Theories permit the derivation of exact renormalization group invariant results also in this sector of the theory. Of particular interest is a RGI sum rule for the soft scalar masses holding to all-orders in perturbation theory. In the case of Finite Unified Theories the sum rule ensures the all-loop finiteness also in their SSB sector and in this way are promoted to completely finite ones. Using the sum rule we investigate the minimal supersymmetric Gauge-Yukawa and two Finite-Gauge-Yukawa SU(5) models. The characteristic features of these models are: a) the old agreement of the top quark mass prediction remains unchanged, b) the lightest Higgs boson is predicted to be around 120 GeV, c) the s-spectrum starts above several hundreds of GeV. (author)