ABSTRACT
With this chapter we start the treatment of non-minimal SUSY models, viewed here from the perspective of an enlarged gauge structure. In fact, we will concentrate on the case of an additional U(1) group above and beyond the SM gauge structure. We will eventually construct the BLSSM (with two possible seesaw realisations) as a phenomenological benchmark for this category of BSM scenarios. Finally, the ESSM will also be introduced. Much of the content of this chapter is based on [21,22,24,228,253].
