Perspectives on Supersymmetry

The following sections are included:

• CONTENTS

• INTRODUCTION

I provide a pedagogical introduction to supersymmetry. The level of discussion is aimed at readers who are familiar with the Standard Model and quantum field theory, but who have little or no prior exposure to supersymmetry. Topics covered include: motivations for supersymmetry; the construction of supersymmetric Lagrangians; supersymmetry-breaking interactions; the Minimal Supersymmetric Standard Model (MSSM); R-parity and its consequences; the origins of supersymmetry breaking; and the mass spectrum of the MSSM.

We give a brief survey of several open theoretical questions in supersymmetric particle physics. The questions we have chosen range from the GeV scale to the Planck scale, and include issues pertaining to the Minimal Supersymmetric Standard Model and its extensions, SUSY-breaking, cosmology, grand unified theories, and string theory. Throughout, our goal is to address those topics in which supersymmetry plays a fundamental role, and which are areas of active research in the field. A more complete discussion of these and other open questions can be found in the e-print hep-ph/9712322.

We review the origin of soft supersymmetry–breaking terms in N = 1 supergravity models of particle physics. We first consider general formulae for those terms in general models with a hidden sector breaking supersymmetry at an intermediate energy scale. The results for some simple models are given. We then consider the results obtained in some simple superstring models in which particular assumptions about the origin of supersymmetry breaking are made. These are models in which the seed of supersymmetry breaking is assumed to be originated in the dilaton/moduli sector of the theory.

We discuss issues that arise in the regularisation of supersymmetric theories.

Supersymmetry was first discovered in string theory. This essay describes how supersymmetry is crucial to our present understanding of string theory, and why if string theory is correct, low energy supersymmetry is a likely consequence.

Searches for supersymmetric particles performed at LEP 1 and LEP 2 are reviewed. Using the MSSM with R-parity conservation as a reference model, the various analyses are briefly described, and the results are presented in terms of mass and coupling limits. Further implications of these results are discussed, including lower limits on the mass of a neutralino LSP, assuming the MSSM with GUT relations. Less conventional scenarii, among which those involving R-parity violation, are also investigated.

We review the status of searches for Supersymmetry at the Tevatron Collider. After discussing the theoretical aspects relevant to the production and decay of supersymmetric particles at the Tevatron, we present the current results for Runs Ia and Ib as of the summer of 1997.

We classify the variety of low-energy supersymmetric signatures that can be probed at future colliders. We focus on phenomena associated with the minimal supersymmetric extension of the Standard Model. The structure of the supersymmetry-breaking introduces additional model assumptions. The approaches considered here are supergravity-mediated and gauge-mediated supersymmetry-breaking. Alternative phenomenologies arising in non-minimal and/or R-parity-violating approaches are also briefly examined.

Models of particle physics that include weak scale supersymmetry predict a rich spectra of new particle states lying at or below the TeV energy scale. These new states ought to be accessible to present or future collider experiments. Event generator programs provide the crucial tool for linking models of weak scale supersymmetry to collider search experiments. In this chapter we discuss the current status of event generator ISAJET and PYTHIA programs. In addition, we show how these can be used for collider searches at e⁺e^-, or pp colliders. As examples, we show for several popular models the regions of parameter space where SUSY signals ought to be discoverable above Standard Model backgrounds for the LEP2, Tevatron, LHC and NLC colliders.

The lightest supersymnietric particle (LSP) is stable in an R-parity conserving theory. In this article the steps needed to calculate the present day mass density of such a particle are detailed. It is shown that there can be a significant amount of LSP dark matter in the universe. Furthermore, relic abundance considerations put an upper bound on how large supersymmetry breaking masses can be without resorting to finetuning arguments.

Inflation is a promising solution to many problems of the standard Big-Bang cosmology. Nevertheless, inflationary models have proved less compelling. In this chapter, we discuss why supersymmetry has led to more natural models of inflation. We pay particular attention to multifield models, both with a high and a low Hubble parameter.

We review the status of heavy neutral gauge bosons, Z', with emphasis on constraints that arise in supersymmetric models, especially those motivated from superstring compactifications. After elaborating on the status and (lack of) predictive power for general models with an additional Z', we concentrate on motivations and successes for Z' physics in supersymmetric theories in general and in a class of superstring models in particular. We review phenomenologically viable scenarios with the Z' mass in the electroweak or in the intermediate scale region.

We discuss the prospect of studying physics at short distances, such as Planck length or GUT scale, using supersymmetry as a probe. Supersymmetry breaking parameters contain information on all physics below the scale where they are induced. We will gain insights into grand unification (or in some cases string theory) and its symmetry breaking pattern combining measurements of gauge coupling constants, gaugino masses and scalar masses. Once the superparticle masses are known, it removes the main uncertainty in the analysis of proton decay, flavor violation and electric dipole moments. We will be able to discuss the consequence of flavor physics at short distances quantitatively.

If the LSP were (mainly) a higgsino the signatures of several superpartners (but not all) at colliders would involve isolated photons. Some possible superpartner candidates at LEP and FNAL are characterized by such photons. If the associated sparticles are indeed light (and if there is a light stop), one expects small effects in b → s + γ, R_B, and α_s — the reported data is a little more consistent with what is expected in a higgsino-LSP world than with the SM. The resulting LSP is a good cold dark matter candidate, and the sparticles have properties that allow EW baryogenesis. Each of these phenomena only can be evidence for supersymmetry if tan β,μ and gaugino masses M₁ and M₂ have certain values, and the whole picture can only be right if the resulting values are the same for all phenomena. The expected behavior of superpartners at colliders is quite different from the usual (Bino-LSP) case studied. There will be a number of tests possible at LEP and FNAL.

We review the status of theories with gauge-mediated supersymmetry breaking.

The presence of scalar fields with color and electric charge in supersymmetric theories makes feasible the existence of dangerous charge and color breaking (CCB) minima and unbounded from below directions (UFB) in the effective potential, which would make the standard vacuum unstable. The avoidance of these occurrences imposes severe constraints on the supersymmetric parameter space. We give here a comprehensive and updated account of this topic.

We review the loop effects of the low energy supersymmetry. The global success of the Standard Model rises two related questions: how strongly the mass scales of the superpartners are constrained and can they be, nevertheless, indirectly seen in precision measurements. The bulk of the electroweak data is well screened from supersymmetric loop effects, due to the structure of the theory, even with super-partners generically light, . The only exception are the left-handed squarks of the third generation which have to be to maintain the success of the SM. The other superpartners can still be light, at their present experimental mass limits, and would manifest themselves through virtual corrections to the small number of observables such as R_b, b → sγ, and mixing and a few more for large tan β. Those effects require still higher experimental precision to be detectable.

We discuss CP violation in the context of the minimal SUSY extension of the standard model as well as in a generic low-energy SUSY model. After analyzing the SUSY contributions to the observed CP violation in the kaon system, we emphasize the prospects for disentangling SUSY loop contributions from pure SM effects in B physics.

The development of supergravity unified models and their implications for current and future experiment are discussed.

I discuss the theoretical motivations for R-parity violation, review the experimental bounds and outline the main changes in collider phenomenology compared to conserved R-parity. I briefly comment on the effects of R-parity violation on cosmology.