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Taking SUSY One Step Further

Supersymmetry (SUSY), the idea that there is a symmetry between bosons and fermions, is perhaps the most popular framework for new physics beyond the Standard Model. SUSY predicts that every Standard Model particle has an as-yet undiscovered "superpartner." Proponents of the theory believe that these particles will appear at the Large Hadron Collider (LHC) at CERN. Determining whether low-energy SUSY exists will be a major goal of the LHC; if discovered, the study of these particles will become a major activity in high-energy physics.

It is not enough, though, simply to discover the SUSY particles (or "sparticles"). SUSY would imply a major extension of the fundamental laws of nature. It would give us new principles with which to understand the other elementary particle interactions, and it might also give us a particle that makes up the dark matter. To learn how the new laws of SUSY operate, we need to measure the masses and properties of the sparticles as accurately as possible.

The SUSY model which contains the standard model, but which adds the fewest new particles, is the Minimal Supersymmetric Standard Model (MSSM). This is not a simple model. It contains some 105 new parameters (beyond the 20 free parameters in the Standard Model). These fundamental parameters determine the masses and couplings of the sparticles and also answer questions about the role of SUSY in the weak interactions, the mass generation for the quark and leptons, and the properties of dark matter. Most of these parameters must be very small to avoid unwanted effects in B physics and Charge Parity (CP) violation. This leaves about 20 new parameters that will be important and must be determined.

We expect to learn a great deal about SUSY at the LHC, but it seems unlikely that we will be able to determine this full set of parameters from the LHC data alone. In a recent paper, Nima Arkani-Hamed, Gordon Kane, Jesse Thaler, and Lian-Tao Wang found examples in which totally different sets of MSSM parameters give indistinguishable experimental signatures at the LHC. They called this problem the "LHC Inverse Problem." This problem is not new to people who have been thinking about future electron–positron colliders.

In fact, the ability of experiments at e+e- colliders to measure subtle properties of SUSY and other possible new particles is one of the main motivations for building the International Linear Collider (ILC). In the past few years, it has been realized that the question of whether the lightest SUSY particle can be dark matter hinges on the details of this particle's interactions, details that are especially difficult to determine at the LHC but which should be visible in ILC experiments.

The points in MSSM parameter space (which we call "models" for brevity) studied by Arkani-Hamed and his colleagues also provide challenges for e+e- experiments. To clarify what the ILC can do for these models, a group of us—Ben Lillie, now at Argonne, and Carola Berger, JoAnne Hewett, Tom Rizzo and I—have been studying these models in detail. We have been able to take advantage of the simulation tools for the ILC and the SiD detector that have been built here at SLAC by Norman Graf and his group. We have also made use of the detailed set of Standard Model backgrounds at the ILC that Tim Barklow has assembled for ILC studies. In all, looking at especially difficult SUSY models in the context of realistic detection and backgrounds, our study has become a test of the capabilities of ILC and SiD.

The models we have looked at are especially difficult when compared with the standard "benchmark" SUSY points for several reasons. Most importantly, in most of the models we considered there are very few sparticles which are light enough to be produced at 500 GeV, the design energy of the ILC. Further the mass differences between these particles and the lightest supersymmetric particle, which in the MSSM is absolutely stable, are often small. As a result of these features, many of the analyses in the literature for detecting and measuring the properties of sparticles are inadequate for our purposes. We therefore have spent a great deal of time and effort designing new analyses for these more difficult, but possibly more realistic, SUSY models.

Of the 242 models which, in the analysis of Arkani-Hamed, Kane, Thaler, and Wang, have experimental signatures indistinguishable at the LHC, 84 have a charged sparticle accessible at 500 GeV. We have now learned how to actually detect the signal of supersymmetry in about 80% of these models. The remaining models are the especially tough cases. About half involve strong suppression of the production rate for the sparticles, for example, because the sparticles are very close to their kinematic threshold. In the other half, the only accessible sparticle is a stau, the superpartner of the tau lepton. The stau must be observed by reconstructing the tau. This introduces extra uncertainty and makes it difficult to observes staus with certain properties. We are just beginning to explore the question of distinguishing the pairs of models. In many cases, the distinction is obvious once the sparticles are observed, but other cases are more challenging.

No one knows for sure whether SUSY exists, or whether the MSSM is the correct model for SUSY even if SUSY exists. Also, even if the MSSM is realized in nature, no one knows whether its parameters resemble a benchmark SUSY point with many light, accessible sparticles, or one of the models we studied, in which the sparticles are much harder to detect. Thus it is important to have detailed studies for both possibilities, in order to better prepare detectors and analyses for the ILC. We hope our work contributes to this important effort.

James Gainer, SLAC Today, September 6, 2007