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Supersymmetric Dark Matter SUPERSYMMETRIC DARK MATTER G. JUNGMAN”, M. KAMIONKOWSKIb,“, K. GRIESTd a Department of Physics, Syracuse University, Syracuse, NY 13244, USA. [email protected] b Department of Physics, Columbia University, New York, NY 10027, USA. [email protected] ’ School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540, USA ‘Departm e n t of Ph y sits, University of California, San Diego, La Jolla, CA 92093, USA. [email protected] ELSEVIER AMSTERDAM - LAUSANNE - NEW YORK - OXFORD 2 SHANNON - TOKYO PHYSICS REPORTS ELSEWIER Physics Reports 267 (1996) 195-373 Supersymmetric dark matter Gerard Jungmana, Marc Kamionkowskib,“, Kim Griestd aDepartment of Physics, syyacuse University, Syracuse, NY 13244, USA. [email protected], bDepartment of Physics, Columbia University, New York, NY 10027, USA. [email protected], ‘School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540. USA, a Department of Physics, University of California, San Diego, La Jolla, CA 92093, USA. [email protected] Received June 1995; editor: D.N. Schramm Contents 1. Introduction 198 6.4. Fermion final states 252 2. Dark matter in the Universe 206 6.5. Gluon final states 256 2.1. Inventory of dark matter 206 6.6. Photon final states 258 2.2. Theoretical arguments 209 6.7. Summary of neutralino annihilation 259 2.3. Baryonic content of the Universe 211 7. Elastic-scattering cross sections 260 2.4. Distribution of dark matter in the Milky 7.1. The basic ingredients 260 Way 211 7.2. Axial-vector (spin) interaction 261 2.5. Overview of dark-matter candidates 216 7.3. Scalar interaction 266 3. Cosmological abundance of a WIMP 218 7.4. General axial-vector, vector, and scalar 3.1. Simple estimates 218 interactions 273 3.2. Why WIMPS? 222 7.5. Comparison of spin and scalar cross 3.3. Standard calculation of relic abundance 222 sections 274 3.4. Special cases 223 8. Direct detection of neutralinos 276 3.5. Possible loopholes 22.5 8.1. Theory 276 3.6. Constraints on the WIMP density 226 8.2. Detectors 283 4. Supersymmetric models 227 8.3. Inelastic-scattering techniques 286 4.1. Motivation, goals, and some formalities 227 9. Energetic neutrinos from WIMP annihilation 4.2. Minimal supersymmetric standard model 231 in the Sun and/or Earth 287 4.3. SUSY-GUT and supergravity models 234 9.1. General description 287 5. Laboratory constraints 238 9.2. Detectors and atmospheric-neutrino 5.1. Remarks 238 background 290 5.2. Constraints on the Higgs sector 238 9.3. Annihilation rate in the Sun and Earth 292 5.3. Constraints on the chargino/neutralino 9.4. Capture rate in the Sun and Earth 294 sector 239 9.5. Neutrino spectra 302 5.4. Sleptons 239 9.6. Model-independent analysis and summary 308 5.5. Squarks and gluinos 240 9.7. Comparison of direct and indirect 5.6. Limits from rare processes 240 detection 312 6. Neutralino annihilation 244 10. Cosmic rays from WIMP annihilation 6.1. Remarks 244 in the halo 315 6.2. Weak gauge-boson final states 246 10.1. Cosmic-ray antiprotons 316 6.3. Final states containing Higgs bosons 248 10.2. Cosmic-ray positrons 318 0370-1573/96/$32.00 0 1996 Elsevier Science B.V. All rights reserved SSDZ 0370-1573(95)00058-5 G. Jungman et al. /Physics Reports 267 (1996) 195-373 197 10.3. Cosmic gamma rays 319 13. Conclusions 337 11. Sample analysis of the MSSM 322 13.1. Summarv of calculations 337 11.1: Orientation 322 13.2. Central iesults 340 11.2. SUSY parameter space 323 13.3. Concluding remarks 340 11.3. Relic density 325 Appendix A. Construction of the MSSM 342 11.4. Elastic-scattering cross sections 326 A. 1. Introduction 342 11.5. Direct-detection rates 327 A.2. Superfield formalism 342 11.6. Indirect-detection rates 332 A.3. Minimal supersymmetric standard model: 11.7. Comparison of direct and indirect rates 333 general discussion 343 11.8. Results from unified models 333 A.4. Minimal supersymmetric standard model: 12. Other particle dark-matter candidates 334 spectrum and interactions 347 12.1. The rise and fall of heavy-neutrino dark AS. SUSY-GUT and supergravity models 360 matter 334 A.6. Parameterizations 361 12.2. Sneutrinos 336 Appendix B. User’s guide for Neutdriver 363 12.3. Other supersymmetric dark-matter References 364 candidates 336 Abstract There is almost universal agreement among astronomers that most of the mass in the Universe and most of the mass in the Galactic halo is dark. Many lines of reasoning suggest that the dark matter consists of some new, as yet undiscovered, weakly interacting massive particle (WIMP). There is now a vast experimental effort being surmounted to detect WIMPS in the halo. The most promising techniques involve direct detection in low-background laboratory detectors and indirect detection through observation of energetic neutrinos from annihilation of WIMPS that have accumulated in the Sun and/or the Earth. Of the many WIMP candidates, perhaps the best motivated and certainly the most theoretically developed is the neutralino, the lightest superpartner in many supersymmetric theories. We review the minimal supersymmetric extension of the standard model and discuss prospects for detection of neutralino dark matter. We review in detail how to calculate the cosmological abundance of the neutralino and the event rates for both direct- and indirect-detection schemes, and we discuss astrophysical and laboratory constraints on supersymmetric models. We isolate and clarify the uncertainties from particle physics, nuclear physics, and astrophysics that enter at each step in the calculations. We briefly review other related dark-matter candidates and detection techniques. 198 G. Jungman et al. /Physics Reports 267 (1996) 195-373 1. Introduction In recent years, there has been a growing interaction between particle physics and astrophysics. The theoretical interest lies in the potential for particle-physics ideas to explain some of the thornier problems of cosmology, and the potential for astrophysical and cosmological observa- tions to constrain ideas in particle physics. Although particle astrophysics was initially often dominated by theoretical speculation, it has recently reached a new level of maturity due to an active experimental thrust. In some areas, the connection between particle physics and astrophysics has become increasingly precise, and astrophysics has been able (or will soon be able) to provide empirical information that complements the results of accelerator experiments. The link between supersymmetry and dark matter is exemplary. In this review, we will explore the details of this link. The standard model of particle physics provides an excellent description of physical processes at energies thus far probed by experiments. This includes those energies available in accelerator experiments, as well as those probed by measurements of, or bounds on, rare processes. Yet, virtually every particle theorist will agree that physics beyond the standard model is likely. In particular, new phenomena may well appear at the electroweak scale. Unitarity of electroweak interactions breaks down at energy scales 5 O(TeV) in the absence of a mechanism to account for electroweak-symmetry breaking. In the minimal model, electroweak symmetry is broken with a single Higgs doublet. Although consistent at low energies, the existence of a fundamental scalar field in the theory (the Higgs field) leads to an instability at higher energies, requiring a fine tuning of the high-energy parameters. Furthermore, the gauge structure in the standard model suggests the existence of a grand unified theory (GUT) at an energy scale of roughly 1016 GeV. Finally, there is the question of a more fundamental theory which would include quantum gravitational effects, presumably becoming strong at the Planck scale, 1019 GeV. Thus it seems quite possible that the standard SU(3) x SU(2) x U(1) model for particle interactions is a low-energy limit of some underlying theory whose true structure will only become apparent when higher-energy scales are probed. When Dirac combined special relativity with quantum mechanics, his equation contained a new charge-conjugation symmetry which required the existence of an antiparticle for each known particle. Dirac’s initial hope that the electron might be the partner of the proton was soon dashed, but the discovery of the positron vindicated Dirac’s theory. Today, this “doubling” of the number of particles is taken for granted to such an extent that antiparticles are not generally listed in the particle data book [l]. It is interesting that attempts to combine general relativity with quantum field theory (through the introduction of local supersymmetry) can lead to a supersymmetric doubling of the number of particles. Here, the symmetry relates bosonic integral-spin particles to fermionic half-integral-spin superpartners and vice versa. The discovery of supersymmetric part- ners has not followed quickly behind the theory, as did the discovery of the positron, although the hypothetical particles have been thoroughly studied. Searches for these particles are taking place at all the major accelerators. Examples of superpartners are the squarks and sleptons, the spin-0 partners of the quarks and leptons, and neutralinos, the spin-4 Majorana particles which are linear combinations of the supersymmetric partners of the photon, Z” and Higgs bosons (e.g., photino, higgsino, Z-ino). Supersymmetry (SUSY) is an ingredient that appears in many theories for physics beyond the standard model. This is primarily because supersymmetry can cure the theoretical difficulty of G. Jungman et aLlPhysics Reports 267 (1996) 195-373 199 fundamental scalar particles which was mentioned above; it can render a theory stable to the radiative corrections which would otherwise force a fine tuning of high-energy parameters. This instability is the infamous “naturalness” problem (see, e.g., [2]), and we will discuss this technical point in Section 4.
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