At this point, we have all the ingredients necessary for constructing a supersymmetric version of the Standard Model, complete with explicit soft SUSY breaking terms. The simplest such model, known as the Minimal Supersymmetric Standard Model, or MSSM, is a direct supersymmetrization of the Standard Model (except for the fact that one needs to introduce two Higgs doublet fields). It is minimal in the sense that it contains the smallest number of new particle states and new interactions consistent with phenomenology.

To construct the MSSM, we follow the recipe for the construction of supersymmetric gauge theories at the end of Chapter 6 and proceed as follows:

1. We choose the gauge symmetry group for the theory to be the Standard Model gauge group, SU(3)C × SU(2)L × U(1)Y.

2. We select the matter content of the theory, to be realized as left-chiral scalar superfields, with gauge quantum numbers exactly as in the Standard Model. The Higgs sector is chosen to consist of two left-chiral scalar superfields with opposite hypercharge.

3. We choose the form of the superpotential.

4. Finally, we compute the supersymmetric Lagrangian using the master formula Eq. (6.44), and augment it by all possible soft SUSY breaking terms consistent with the gauge and Poincaré symmetries as discussed in Chapter 7.

Constructing the MSSM

As mentioned, we choose the gauge symmetry of the Standard Model: SU(3)C × SU(2)L × U(1)Y. The gauge bosons of the SM are promoted to gauge superfields.

Once sparticles are produced, they will typically decay into another sparticle together with SM particles via many different channels. The daughter sparticles subsequently decay to yet lighter sparticles until the decay cascade terminates in the stable LSP. In this discussion we have implicitly assumed that R-parity is conserved: otherwise, sparticles may also decay into just SM particles, and the final state would be comprised of only SM particles. However, whether or not R-parity is conserved, sparticle production at colliders typically leads to a variety of final state topologies via which to search for SUSY. Signal rates into any particular topology are determined by sparticle production cross sections studied in the last chapter, and by the branching fractions for various decays of sparticles.

In this chapter, we examine sparticle decays in the context of the R-parity conserving MSSM. As just mentioned, R-parity conservation implies that any sparticle decay chain will end in a stable LSP which may be a neutralino, a sneutrino, or, in models with local supersymmetry, also a gravitino. We have already seen in Chapter 9 that a sneutrino LSP is disfavored. A weak scale gravitino is essentially decoupled as far as collider physics considerations go. Hence, for most of this chapter, we will assume the gravitino is unimportant for sparticle decay calculations. However, as we saw in Section 11.3.1, an important exception to this occurs if the scale of SUSY breaking is low so that gravitinos are very light. To cover this possibility, we address sparticle decays to gravitinos in the last section of this chapter.

Supersymmetry (SUSY) is a lovely theoretical construct, and has captured the imagination of many theoretical physicists. It allows for a new synthesis of particle interactions, and offers a new direction for the incorporation of gravity into particle physics. The supersymmetric extension of the Standard Model also ameliorates a host of phenomenological problems in the physics of elementary particles, if superpartners exist at the TeV scale. These new states may well be discovered in experiments at high energy colliders or in non-accelerator experiments within the next few years!

There are several excellent books that explore the theoretical structure of supersymmetry. These advanced texts are rather formal, and focus more on the theoretical structure rather than on the implications of supersymmetry. This makes them somewhat inaccessible to a large number of our experimental as well as phenomenological particle physics colleagues, working on the search for the new particles predicted by supersymmetry. Our goal in this book is to provide a comprehensive (and comprehensible) introduction to the theoretical structure of supersymmetry, and to work our way towards an exploration of its experimental implications, especially for collider searches. Although we have attempted to orient this book towards experimentalists and phenomenologists interested in supersymmetry searches, we hope that others will also find it interesting. In particular, we hope that it will provide theorists with an understanding and appreciation of some of the experimental issues that one is confronted with in the search for new physics.

We use the language of four-component relativistic spinors throughout this text, rather than the sometimes more convenient approach using two-component spinors.

While the first clear hints of deviation from the SM may well come from any of a large variety of experiments, establishing precisely what the new physics is will be possible only by observations at energy scales close to, or beyond, the threshold for the new phenomena. Direct examination of the properties of any new states of matter associated with the new physics is probably the best way to study the new phenomena, if these degrees of freedom are kinematically accessible. If the new physics is supersymmetry, then the new states of matter will be the superpartners, and it is only by determining their quantum numbers and couplings that we can unambiguously establish that the new physics is actually supersymmetry. Of course, any new states of matter may be quite different from superpartners. For instance, if extra spatial dimensions exist which are accessible at the weak scale, the new degrees of freedom will be Kaluza–Klein excitations of SM particles. It is even possible that no new degrees of freedom are directly accessible, but that SM interactions acquire form factors that point to what the new physics might be. Our point here is that elucidation of new physics will only be possible at colliding beam facilities.

The purpose of this chapter is to examine what may be learned from a study of high energy collisions assuming that nature is supersymmetric at the weak scale. To start with, we review various searches for supersymmetry in previous collider and fixed target experiments.

We know that the superpartners of SM particles must acquire SUSY breaking masses, since otherwise they would have been produced in experiments via their gauge interactions. This requires an understanding of the mechanism of supersymmetry breaking. A variety of models for supersymmetry breaking have been postulated in the literature. The general consensus seems to be that the SM superpartners cannot acquire tree-level masses via spontaneous breaking of global supersymmetry at the TeV scale: we have seen in Chapter 7 that this leads to phenomenological problems with tree-level sum rules which imply that some sfermions must be lighter than fermions. Within the framework of the MSSM our ignorance of the SUSY breaking mechanism is parametrized by 178 soft SUSY breaking parameters.

The MSSM is, therefore, regarded as a low energy effective theory to be derived from a theory that incorporates supersymmetry breaking. In the next chapter, we will discuss various models for the generation of soft SUSY breaking parameters that have been suggested in the literature. These models circumvent the problems with the sum rules in one of two different ways. Either the models are based on local supersymmetry, or the soft SUSY breaking parameters are generated only at the loop level. As preparation for a discussion of the first of these classes of models, in this chapter we present a short discussion of locally supersymmetric theories where the parameters of SUSY transformations depend on the spacetime co-ordinates. Since supersymmetry is a spacetime symmetry, local supersymmetry necessarily involves gravitation. Local supersymmetry is, therefore, also referred to as supergravity. Supergravity is a large and complex subject in its own right, and its elaboration is beyond the scope of this book.

Almost no one doubts that the Standard Model is only an effective theory that has to be incorporated into a larger framework. What this framework will ultimately look like, we do not know. Empirical facts that we cannot account for in the Standard Model, such as neutrino masses, dark matter, and dark energy, provide some guidance. Aesthetic considerations such as the desire for unification of interactions and for an understanding of the patterns of matter fermion masses and mixing angles also guide our thinking. Although this seems rather removed from particle physics today, we also hope that one day we will have a framework that consistently incorporates gravity.

It was, however, efforts to resolve the fine-tuning problem of the Standard Model that led us to arrive at the exciting conclusion that there must be new physics at the TeV scale that can be probed at high energy colliders such as the LHC or a TeV electron–positron linear collider. Weak scale supersymmetry provides an attractive resolution of this problem, and continues to hold promise also for several other reasons, detailed at the end of Chapter 2. Indeed, many of these positive aspects of supersymmetric models have become evident only in the last 10–15 years – many years after the discovery of supersymmetry, and well after the effort to explore its phenomenological implications had begun in earnest. We believe that the motivations for seriously examining supersymmetry remain as strong as ever.

These promising features notwithstanding, SUSY is not a panacea.

In this chapter, we discuss various implications of the MSSM relevant to low energy experiments in particle physics and to cosmology. We will postpone examination of signals from direct production of sparticles at high energy colliders to later chapters.

In any theory (like the MSSM) with many scalar fields, there are potentially new sources of flavor-changing neutral currents (FCNC). Experiment tells us that such flavor-violating effects are strongly suppressed. Experimental constraints on these restrict the form of soft SUSY breaking masses and couplings in the MSSM. As we will discuss in more detail, viable models may be classified by the pattern (universality, alignment or decoupling) of scalar mass matrices. We also discuss constraints from potentially large CP-violating processes such as the electric dipole moment of the electron and neutron.

We then proceed to study the effects of renormalization in the MSSM, which differ from corresponding effects in the SM because of the presence of weak scale superpartners. The prediction of gauge coupling unification in the MSSM – but not in the SM – is the best known, and perhaps the most spectacular, of these differences. It is possible to view the MSSM as a theory defined at the scale MSUSY ∼ Mweak, but with > 100 additional parameters that have well-defined values at that scale. However, since the MSSM is stable against radiative corrections, it may be valid up to much larger energy scales, perhaps as high as those associated with grand unification or string phenomena. New physics at these scales may provide an organizing principle that determines the multitude of weak scale SUSY parameters in terms of a few more fundamental parameters.