Phenomenological Consequences of Supersymmetric Theories from Dimensional Reduction and Reduction of Couplings

Abstract

The reduction of couplings idea consists in the search for renormalization group invariant relations between seemingly independent parameters of a theory that hold to all orders of perturbation theory. This concept can be applied to $N=1$ GUTs and make them all-loop finite. In the first part of this thesis, after a review of the reduction of couplings method and the properties of finiteness, four models are analysed: a reduced version of the minimal $N=1$ $SU(5)$, a finite $N=1$ $SU(5)$, a two-loop finite $N=1$ $SU(3)^3$ and a reduced version of the MSSM. An update in the phenomenological evaluation is the improved light Higgs-boson mass prediction as provided by the FeynHiggs code. The first three models predict heavy SUSY spectra (produced using the FeynHiggs and SPheno codes) that start just above the TeV scale, consistent with the non-observation LHC results, while the reduced MSSM results in a pseudoscalar Higgs boson mass $M_A$ that is ruled out by recent results of the ATLAS experiment. The three models have very dim prospects of discovery at the HL-LHC. The FCC-hh, however, could be able to test large parts of their predicted spectra. In the second part of the thesis, after a review of the Coset Space Dimensional Reduction, an extension of the SM is presented that results from the dimensional reduction of the $N=1$, $10D$ $E_8$ group over a $M_4 \times B_0/ \mathbf{Z}_3 $ space, where $B_0$ is the nearly-K\"ahler manifold $SU(3)/U(1)\times U(1)$ and $\mathbf{Z}_3$ is a discrete group on $B_0$. Using the Wilson breaking mechanism we get a $4D$ $N=1$ $SU(3)^3$ model plus two global $U(1)$s. Below the GUT scale we have a two Higgs doublet model in a split-like SUSY version of the SM which is phenomenologically consistent, since it produces masses of the top, bottom and light Higgs particles within the experimental limits and predicts the LSP $\sim 1500 GeV$.