Higgs, Top, and Bottom Mass Predictions in Finite Unified Theories

All-loop Finite Unified Theories (FUTs) are N = 1 supersymmetric Grand Unified Theories (GUTs) based on the principle of reduction of couplings, which have a remarkable predictive power. The reduction of couplings implies the existence of renormalization group invariant relations among them, which guarantee the vanishing of the beta functions at all orders in perturbation theory in particular N = 1 GUTs. In the soft breaking sector these relations imply the existence of a sum rule among the soft scalar masses. The confrontation of the predictions of a SU(5) FUT model with the top and bottom quark masses and other low-energy experimental constraints leads to a prediction of the light Higgs-boson mass in the rangeMh ∼ 121−126 GeV, in remarkable agreement with the discovery of the Higgs boson with a mass around ∼ 125.7 GeV. Also a relatively heavy spectrum with coloured supersymmetric particles above ∼ 1.5 TeV is predicted, consistent with the non-observation of those particles at the LHC.