Reduction of Couplings and its application in a Finite Unified Theory and the MSSM

The search for relations among parameters that are renormalization group invariantto all orders in perturbation theory is the basis of the reduction of couplings idea. Thismethod has been applied to someN= 1 supersymmetric Grand Unified Theories, fewof which can become all-loop finite. We review the basic idea and the tools developed,as well as two resulting theories in which reduction of couplings has been achieved: (i)an all-loop finiteN= 1SU(5) model and (ii) a reduced version of the Minimal Super-symmetric Standard Model. We present three benchmark scenarios for the finiteSU(5)model and investigate their observability at existing and future hadron colliders. Themodel’s heavy supersymmetric spectrum lies beyond the reach of the 14 TeV HL-LHC.Concerning the 100 TeV FCC-hh, it is found that large parts of the predicted spectrumcan be tested, but the higher mass regions are beyond the reach even of the FCC-hh. Itis also found that the reduced version of the MSSM is ruled out by the LHC searches forheavy neutral MSSM Higgs bosons for the allowed parameter space.