Reduction of Couplings: Applications in Finite Theories and the MSSM

The method of reduction of couplings is applied to a Finite Unified Theory and in the MSSM.We search for renormalization group invariant relations among couplings of a renormalizable theory which holds to all orders in perturbation theory. The method leads to relations, at the unification scale, between gauge and Yukawa couplings (in the dimensionless sectors of the theory) and relations among the couplings of the trilinear terms and the Yukawa couplings, as well as a sum rule among the scalar masses and the gaugino mass (in the soft breaking sector). In the Finite Unified Theory model we predict, with remarkable agreement with the experiment, the masses of the top and bottom quarks while our predictions for the light Higgs mass and the rest supersymmetric spectrum masses are in comfortable agreement with the LHC bounds on Higgs and supersymmetric particles. In the case of the reduced MSSM the predictions are less successful but recent improvements in the code used to calculate the Higgs masses give promises for better results.