Supersymmetry Breaking: Models of Gauge Mediation with Gauge Messengers

With the start of the LHC, it becomes increasingly important to understand the experimental signatures that discriminate different extensions of the standard model. Supersymmetry (SUSY), in particular the Minimal Supersymmetric Standard Model (MSSM), is one such extension that is specially attractive by its simplicity and elegance. However, if this symmetry is to be realized in nature, it must be spontaneously broken. In this work we will try to understand the most general way in which SUSY breaking can happen in renormalizable field theories and the implications that this has on the minimal extension of the standard model (MSSM) mass spectrum. The first two chapters are the introductory material: in chapter 1 we will introduce some of the key ideas necessary to understand supersymmetric field theories, and in chapter 2 we will briefly describe the the simplest supersymmetric version of the Standard Model. In chapter 3 we will focus on understanding the role of R-Symmetry breaking in determining the soft terms gauge mediation of supersymmetry breaking (GMSB) can lead to. To do this we consider a model where both R-symmetry and SUSY are spontaneously broken. One starts with the model proposed by Intriligator, Seiberg and Shih (ISS) and adds a (dangerous) marginal operator, which we call a meson deformation. The inclusion of this operator leads to the spontaneous breaking of R-symmetry in the vacuum. One then gauges the SU(5) of flavour and identifies it with the MSSM GUT gauge group, thus implementing GMSB. This was the second explicit example where R-symmetry was spontaneously broken in the vacuum. As in the first, gaugino masses iii turned out to be smaller than naively expected so that a mild splitting between scalar (squark and slepton) and gaugino masses exists. After this, a general argument showed that in fact gaugino masses are always significantly smaller than scalar masses if the universe is perturbatively stable. This arguments suggests that any viable vacuum should be (perturbatively) metastable, as had been previously noticed by Murayama and Nomura. In chapter 4, we try to explore alternatives to this scenario by considering the possibility that the vacuum doesn’t break supersymmetry by F-term vevs alone, but by a having simultaneously non-zero F and D-terms. It turns out that this does not happen in models where the Kahler potential is canonical, and the superpotential is a cubic polynomial in the fields, but it can happen if either of these constraints is violated. This leads us to consider a particular example, where we study a hidden sector model with SU(3) gauge group, two flavours of quarks and one singlet. The superpotential is the most general consistent with the tree-level symmetries. The R-symmetry is anomalous, however, but one can still derive selection rules that constrain the form of the effective superpotential. The only extra term that is allowed is an instanton induced contribution. This term explicitly breaks the R-symmetry, but the resulting low energy superpotential is not generic and SUSY is still spontaneously broken. While not a complete example of GMSB, this class of hidden sector models is interesting as it does not require metastability: the tension between the spontaneous breaking of an R-symmetry and the massless R-axion is bypassed by the naturally non-generic superpotential. These models usually have both F and D-term SUSY breaking, but these two vevs are not independent: in non-Abelian theories, the D-term vevs can only be induced by the F-term vevs of fields that are not gauge singlets. The implementation of GMSB in scenarios where the F-terms are not gauge singlets is then considered in both its direct and semi-direct forms: iv In chapter 5 we deal with direct gauge mediation with gauge messengers. In this version of gauge mediation, the spontaneously broken gauge group is identified with the MSSM GUT gauge group and generically leads to tachyonic squark or slepton masses. In the particular case where the GUT gauge group is SU(5), we show that this problem can be solved if there are two independent sectors where SUSY is spontaneously broken or simply by using a solution of the doublet-triplet splitting problem where the vev responsible for the spontaneous breaking of the GUT symmetry is larger than the SUSY breaking scale. In both cases the effects gauge and non-gauge messengers have to combine if a viable spectrum is to be reached. We then finish out study in chapter 6 by considering the semi-direct version of gauge mediation with gauge messengers. As it is known, gaugino masses are screened from messenger interactions, at leading order in the SUSY breaking parameter F. Because of this, gaugino soft masses will be suppressed with respect to scalar soft masses. This leads to a scenario of mildly split SUSY, i.e. scalars are at least one or two orders of magnitude heavier than gauginos. This generically leads to some extra fine-tuning to get the EW breaking scale to occur at the correct scale