Updates and New Results in Models with Reduced Couplings

The idea of reduction of couplings consists in searching for renormalization group invariant relations between parameters of a renormalizable theory that hold to all orders of perturbation theory. Based on the principle of the reduction of couplings, one can construct Finite Unified Theories which are supersymmetric Grand Unified Theories that can be made all‐order finite. The prediction of the top quark mass well in advance of its discovery and the prediction of the light Higgs boson mass in the range GeV much earlier than its discovery are among the celebrated successes of such models. Here, after a brief review of the reduction of couplings method and the properties of the resulting finiteness in supersymmetric theories, we analyse four phenomenologically favoured models: a minimal version of the , a finite , a finite model and a reduced version of the Minimal Supersymmetric Standard Model. A relevant update in the phenomenological evaluation has been the improved light Higgs‐boson mass prediction as provided by the latest version of FeynHiggs. All four models predict relatively heavy supersymmetric spectra that start just below or above the TeV scale, consistent with the non‐observation LHC results. Depending on the model, the lighter regions of the spectra could be accessible at CLIC, while the FCC‐hh will be able to test large parts of the predicted spectrum of each model. The lightest supersymmetric particle, a neutralino, is considered as a cold dark matter candidate and put to test using the latest MicrOMEGAs code.