Heinemeyer, Sven; Mondragón, Myriam; Patellis, Gregory; Tracas, Nicholas; Zoupanos, George The LHC Higgs boson discovery: updated implications for finite unified theories and the SUSY breaking scale. (English) Zbl 1392.81239 Symmetry 10, No. 3, Article ID 62, 26 p. (2018). Summary: Finite Unified Theories (FUTs) are \(N=1\) supersymmetric Grand Unified Theories, which can be made finite to all orders in perturbation theory, based on the principle of the reduction of couplings. The latter consists of searching for renormalization group invariant relations among parameters of a renormalizable theory holding to all orders in perturbation theory. FUTs have proven very successful so far. In particular, they predicted the top quark mass one and half years before its experimental discovery, while around five years before the Higgs boson discovery, a particular FUT was predicting the light Higgs boson in the mass range \(\sim 121-126\) GeV, in striking agreement with the discovery at LHC. Here, we review the basic properties of the supersymmetric theories and in particular finite theories resulting from the application of the method of reduction of couplings in their dimensionless and dimensionful sectors. Then, we analyze the phenomenologically-favored FUT, based on \(\mathrm{SU}(5)\). This particular FUT leads to a finiteness constrained version of the Minimal SUSY Standard Model (MSSM), which naturally predicts a relatively heavy spectrum with colored supersymmetric particles above 2.7 TeV, consistent with the non-observation of those particles at the LHC. The electroweak supersymmetric spectrum starts below 1 TeV, and large parts of the allowed spectrum of the lighter might be accessible at CLIC. The FCC-hhwill be able to fully test the predicted spectrum. MSC: 81V22 Unified quantum theories 81T60 Supersymmetric field theories in quantum mechanics 81R40 Symmetry breaking in quantum theory Keywords:finiteness; supersymmetry; unification; reduction; Gauge-Yukawa; Higgs Software:micrOMEGAs; FeynHiggs PDFBibTeX XMLCite \textit{S. Heinemeyer} et al., Symmetry 10, No. 3, Article ID 62, 26 p. (2018; Zbl 1392.81239) Full Text: DOI arXiv References: [1] Aad, G.; Abajyan, T.; Abbott, B.; Abdallah, J.; Khalek, S.A.; Abdelalim, A.A.; Abdinov, O.; Aben, R.; Abi, B.; Abolins, M.; Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC; Phys. Lett. B: 2012; Volume 716 ,1-29. [2] Chatrchyan, S.; Khachatryan, V.; Sirunyan, A.M.; Tumasyan, A.; Adam, W.; Aguilo, E.; Bergauer, T.; Dragicevic, M.; Erö, J.; Fabjan, C.; Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC; Phys. Lett. B: 2012; Volume 716 ,30-61. 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Phys.: 1999; Volume 38 ,1113-1133. · Zbl 0969.81047 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.