THE NEXT TO MINIMAL SUPERSYMMETRIC STANDARD MODEL WITH A MODERATE STOP MASS

Abstract

In this thesis we analize the Next to Minimal Supersymmetric Standard Model (NMSSM), looking for a natural electroweak symmetry breaking. Focusing on a moderate stop mass and requiring perturbative unification of the gauge couplings (which after all is a very good prediction of the MSSM), we put quite severe restrictions on the parameter space. In particular if we do not modify the theory any further we find that we must live with a small $\kappa\lesssim 0.2$ and $\lambda\lesssim 0.7$. Even in this limit a SM like Higgs boson, which is present in the spectrum, barely touches the LEP2 mass bound. We show that we can improve on this situation if we allow vectorlike multiplets of extra $SU(5)$ symmetric matter to be present at intermediate energies. This matter, while not disturbing unification, allows for a higher value of $\lambda$ at the Fermi scale, in such a way that we are able to obtain a Higgs boson mass as big as $125\, GeV$. At this point we analyze a particular realization of this picture in the corner of the NMSSM parameter space where $\kappa=0$, thus saturating the upper limit on $\lambda$ at the weak scale. Setting to zero the triliner self interaction of the singlet superfield in the superpotential, restores a Peccei-Quinn symmetry in the action which is welcome to solve the $\mu$ problem. A small explicit breaking of such a symmetry is required to give mass to a (pseudo-)Goldstone boson $G$ which would be otherwise experimentally excluded