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From Colliders to Dark Matter SUGRA AND THE STUECKELBERG EXTENSIONS: FROM COLLIDERS TO DARK MATTER A dissertation presented by Daniel J. Feldman to The Department of Physics In partial fulfillment of the requirements for the degree of Doctor of Philosophy in the field of Physics Northeastern University Boston, Massachusetts March, 2009 c Daniel J. Feldman, 2009 ALL! RIGHTS RESERVED SUGRA AND THE STUECKELBERG EXTENSIONS: FROM COLLIDERS TO DARK MATTER by Daniel J. Feldman ABSTRACT OF DISSERTATION Submitted in partial fulfillment of the requirement for the degree of Doctor of Philosophy in Physics in the Graduate School of Arts and Sciences of Northeastern University, March, 2009. Abstract Analyzed in detail are unified models of fundamental interactions based on super- gravity (SUGRA) using effective Lagrangians valid near the grand unification scale, and U(1) extensions of the Standard Model and of its supersymmetric (SUSY) exten- sions where the mass generation of new particle states arises through a Stueckelberg mechanism. Signals of new physics that can be measured at the Large Hadron Col- lider and at the Fermilab Tevatron in various final state channels are discussed in depth. Correlated signals of new physics relevant to both collider experiments and dark matter detection experiments are a focal point of the analysis and the prospects for the discovery of new physics is emphasized. 2 Acknowledgements The work presented here was conducted with my Advisor, Matthews Distinguished Professor Pran Nath (Northeastern University), and with collaborators Dr. Zuowei Liu (Northeastern University and currently of the C.N. Yang Institute, SUNY Stony Brook) and with Dr. Boris K¨ors (at the time at MIT and CERN). I would like to express my gratitude to my Thesis Committee, Professors • Pran Nath, Tom Taylor, and Darien Wood, for their guidance and support. Also, I would like to thank several faculty members at Northeastern for their • help and support over the years including: Professors George Alverson, Arun Bansil, Ella Barberis, Haim Goldberg, Bob Lowndes, Brent Nelson, and Mike Vaughn. I thank the Office of the Provost at Northeastern University, and the Vice- • Provost for Faculty and Graduate Education, Dr. Luis Falc´on, for providing the Dissertation Completion Fellowship during my time of writing this Thesis. In particular I thank Zuowei Liu, who has been a collaborator on much of the • research presented here; a humble friend and a strong colleague. I must single out Professor Pran Nath (PN). • PN, it is an extraordinary privilege to have you as my Advisor. Thank you for your guidance, your time and commitment, and your patience. It is with the greatest level of gratitude that I thank you for the knowledge that you have imparted to me, and for showing me what it means to dedicate oneself to the search for truth in the realm of physics. Finally, I thank my family for their endless encouragement and support. • 3 Contents Abstract 2 Acknowledgements 3 1 Introduction and Overview 7 2 Supersymmetry and Supergravity Unification 11 2.1 A Brief History . 11 2.2 GlobalSUSY ............................... 14 2.3 SUGRA Unification . 16 2.3.1 Low energy realizations . 21 2.3.2 TheSpectra............................ 24 2.3.3 BranchesofREWSB ....................... 26 2.3.4 DarkMatter............................ 28 2.3.5 Sparticle Production at Hadron Colliders ............ 33 3 Towards Decoding the Mechanism for the Origin of Dark Matter 37 3.1 Prelude .................................. 37 3.2 Decoding the Mechanism For Dark Matter Production with the LHC 40 3.2.1 The Chargino Wall and Chargino Ball . 40 miss 3.2.2 Geometry of PT Distributions: . 43 4 3.2.3 P miss as a Discriminator . 44 " T # 3.2.4 Cutting on Jets, njet∗ :....................... 46 3.2.5 Importance of b-Tagging ..................... 48 3.3 Summary ................................. 53 4 Sparticle Landscape and Light Higgses in SUGRA/D-Brane Models 54 4.1 Resolving the Sparticle Landscape . 54 4.2 The Direct Detection of Dark Matter as a Probe of the Landscape . 60 4.3 Higgs Production and B physics . 62 4.4 Light Higgs and D-Branes . 67 4.5 Compressed Spectra in Intersecting D-Brane Models . 70 4.6 The Big Picture . 76 4.7 Summary ................................. 79 Appendix 80 4.8 Appendix: Experimental Constraints . 80 5 The Stueckelberg Mechanism for Mass Generation 84 5.1 The Stueckelberg Extensions of the SM and the MSSM . 87 6 StMSSM : and the XWIMP Stino 88 6.1 TheConnectorSector .......................... 88 6.2 Extra-weak Dark Matter in Z" Models ................. 91 6.2.1 Broken U(1)X with Fayet-Iliopoulos Terms . 91 6.2.2 Stueckelberg Reduction of the U(1)X Extension . 95 6.2.3 Electroweak Constraints on Mixing Parameters . 96 6.2.4 Abelian Extension with Off-Diagonal Kinetic Terms . 97 6.3 Dark Matter from XWIMPs: Relic Density and WMAP Data . 100 5 6.4 Summary ................................. 105 7 Fermilab Probes of a Narrow Z" 106 7.1 Prospects for the Discovery of a Stueckelberg Z" At Fermilab . 111 + 7.1.1 Drell-Yan Cross Section for pp¯ Z" l l− .......... 111 → → 7.1.2 FurtherConstraints fromCDFandDØData. 115 8 Narrow Resonances at the LHC 118 8.1 LHC Observables and Constraints on the StSM Parameter Space . 119 8.1.1 Signal to Background Ratio . 121 8.1.2 How Narrow a Width Can LHC Probe? . 123 8.2 StSM and Massive Graviton at the LHC . 125 8.2.1 MassiveGravitonofWarpedGeometry . 126 8.2.2 Signature Spaces of StSM Z" andoftheGraviton . 128 + 8.2.3 Angular Distributions from pp (Z",G) l l− ........ 131 → → 8.3 Summary ................................. 132 9 Dark Matter from the Hidden Sector 135 9.1 Kinetic and Stueckelberg Mass Mixings . 136 9.2 On the Origin of Milli-Charged Matter ................. 138 9.3 ConstraintsfromElectroweakData . 140 9.4 Milli-charged DM from the Hidden Sector ............... 144 9.5 PAMELA/ATIC & Breit-Wigner Enhancement . 150 9.6 Summary ................................. 156 10 Conclusions 158 Bibliography 163 6 Chapter 1 Introduction and Overview With the coming on-line of the Large Hadron Collider (LHC), we are entering a new and challenging phase in the quest to discover what lies beyond the Standard Model (SM) of particle physics. The LHC may very well provide us with a paradigm shift, opening a new window towards our collective understanding of the nature of fundamental physics. The exploration of the nature of new physics will be further facilitated by astrophysical data. The analysis presented in this Thesis is precisely related to the above. We begin with a brief overview of supergravity unified models (SUGRA) and their low energy realizations. Following this, an analysis is given of the dual probes of su- persymmetry through a simultaneous study of signals relevant to the direct detection of dark matter and from collider signatures of supersymmetry. It is first discussed how the LHC can allow one to decode the mechanism for the origin of dark matter production in the early universe in the framework of SUGRA models. Several cor- related signatures of new physics emerge which allow for a discovery supersymmetry (SUSY) in this framework. The analysis exhibits for the first time in the literature a direct correlation between the signature space of dark matter direct detection and 7 the signature space of LHC signals. Indeed such a mapping between dark matter signatures and LHC signatures leads us to a more general method of pinning down the underlying model and such an approach to studying SUSY may point us to the mechanism for the production of dark matter in the early universe. Next, an analysis is given in SUGRA/Brane models from the perspective of the Sparticle Landscape of Mass Hierarchies. Thus, in models built on the premise of supersymmetry, there is a large landscape of possible sparticle mass hierarchies, but these possibilities reduce drastically in well motivated models where supersymmetry breaking triggers electroweak symmetry breaking and the set of possible mass hier- archies becomes predictive. It is then found more generally that the nature of LHC signatures is correlated very strongly with such mass hierarchies and this is also the case for the predictions of cross sections from the scattering of neutralinos offnuclei which are relevant for dark matter direct detection experiments. Therefore, collider and dark matter experiments get closely tied together more generally. The possibility of relatively light Higgs bosons are also discussed and the convergence of constraints on light Higgses from experimental data is noted. The second part of this Thesis focuses on collider signatures and the implications for dark matter that arise in the Stueckelberg extensions of the Standard Model and its minimal supersymmetric extension. Predictions are made for the discovery potential of narrow resonances at the Tevatron and the LHC and new candidates for dark matter and some of their experimental consequences are analyzed. We elaborate on this a bit further below. In a broad class of models based on grand unification, on strings, and on D-Branes one expects extra Abelian gauge group factors beyond the Standard Model gauge group. It is often the case that one or more of these gauge groups remain unbroken at the grand unified scale or string scale and survive down to the electroweak scale. 8 The breaking of such factors at or near the electroweak scale can generate unexpected new phenomena. An interesting possibility arises when the Abelian gauge group is ’hidden’ i.e. the matter fields in this sector are neutral with respect to the Standard Model (SM). The exploration of these issues can be tackled within certain low energy realizations of strings, in terms of their field theoretic manifestations. An example of this is the inclusion of Stueckelberg mass mixings in the low energy Lagrangian of the SM, as indeed such mass mixings are generic to many classes of string theories.
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