Reduction of Couplings: Finite Unified Theories and the reduced MSSM
2019 September 19
The principle of reduction of couplings, combined with $N=1$ supersymmetry, can lead to realistic quantum field theories, where the gauge and Yukawa sectors are related. It is the basis to find all-loop Finite Unified Theories (FUTs), where the $\beta$-function vanishes to all loops in perturbation theory. It can also be applied to the Minimal Supersymmetric Standard Model (MSSM), leading to an important reduction of the number of parameters. We present results for the $N=1$ $SU(5)$ FUT, the $N=1$ $SU(3)\otimes SU(3)\otimes SU(3)$ FUT and the reduced MSSM. These models lead to successful predictions for the masses of the third generation of quarks and the Higgs boson. They also predict a heavy supersymmetric spectrum, consistent with the non-observation of supersymmetry so far. The FCC-hh will be able to fully test the predicted spectrum.