Finite Unified Theories and the prediction of the Higgs mass

Finite Unified Theories (FUTs) are N=1 supersymmetric Grand Unified Theories, which can be made all-loop finite, both in the gauge and Yukawa couplings and in the soft supersymmetry breaking sector. This remarkable property, based on the reduction of couplings at the quantum level, provides a drastic reduction in the number of free parameters, which in turn leads to predictions for the top and bottom quark masses, as well as predictions for the Higgs boson mass and the supersymmetric spectrum. Here we examine the predictions of two SU(5) FUTs, taking into account a number of theoretical and experimental constraints. We show how the phenomenological constraints can discriminate among the two models, and we give also the above mentioned predictions for the model that complies with all the constraints.