Prediction of the Higgs mass from finite and minimal susy Gauge-Yukawa GUTs

The search for renormalization group invariant (RGI) relations among the couplings of GUTs holding beyond the unification point leads to the predictive scheme of Gauge-Yukawa Unified Theories. In this class of theories, of particular interest are those GUTs which are finite beyond the unification paint even to all orders in perturbation theory, i.e. exactly finite. Extending the search to the soft supersymmetry-breaking (SSB) sector of these theories we obtain exact RGI relations and exact finite theories also in this sector. Taking into account several phenomenological constraints we obtain an accurate prediction of the standard model (SM) Higgs mass in addition to the previous successful prediction of the top quark mass. Another interesting and distinct feature of these models is that their predictions for the spectrum beyond the SM starts above several hundreds of GeV.