Table Of Content

Simulations of R-parity Violating SUSY Models 1 0 0 2 n a J 0 Peter Richardson 1 Balliol College 1 v 5 0 Department of Physics Theoretical Physics 1 · University of Oxford 1 0 1 0 / h p - p e h (cid:1) : v i X r a Thesis submitted in partial fulﬁllment of the requirements for the Degree of Doctor of Philosophy at the University of Oxford August 2000 · · Abstract In recent years there has been a great deal of interest in R-parity violating supersymmetric models. We explain the motivation for studying these models and explore the various phenomenological consequences of R-parityviolation. In particular, we argue that if we are to explore all channels for the discovery of supersymmetry then these models must be investigated. It has become essential for the experimental study of any new model to have a Monte Carloeventgeneratorwhichincludestheprocessespredictedbythatmodel. Wereviewthe techniques used in the construction of these simulations and show how we have extended the HERWIG event generator to include R-parity violating processes. We discuss how to treat the emission of QCD radiation in these processes including colour coherence eﬀects via the angular-ordered parton shower. We then make use of this simulation to investigate the discovery potential for resonant slepton production, via either supersymmetric gauge or R-parity violating decay modes, in hadron–hadron collisions. In particular, we show that although the colour coherence properties of the R-parity violating decay modes can be used to improve the extraction of a signal above the QCD background these processes will only be visible for large values of the R-parity violating Yukawa couplings. However a signal, i.e. like-sign dilepton production, from the supersymmetric gauge decay modes is visible above the background for much smaller values of the R-parity violating Yukawa couplings. Finally, we look at the possibility that the KARMEN time anomaly can be explained by the existence of a light neutralino which is produced in the decay of charged pions via R-parity violation. This neutralino then decays inside the KARMEN detector, into three leptons via R-parity violation, explaining the excess of events observed by the KARMEN experiment. The road goes ever on and on, down from the door where it began, now far ahead the road has gone and I must follow if I can ... J.R.R. Tolkien To my parents, this wouldn’t have been possible without their support and encouragement. Contents Acknowledgments xi 1 Introduction 1 1.1 Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Quantum Chromodynamics . . . . . . . . . . . . . . . . . . . . . . 5 1.1.2 Electroweak Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.1.3 Symmetries of the Standard Model . . . . . . . . . . . . . . . . . . 9 1.2 Supersymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.2.1 Introduction to Supersymmetry . . . . . . . . . . . . . . . . . . . . 11 1.2.2 Motivations for Supersymmetry . . . . . . . . . . . . . . . . . . . . 12 1.2.3 Construction of Supersymmetric Lagrangians . . . . . . . . . . . . 15 1.2.4 The Minimal Supersymmetric Standard Model . . . . . . . . . . . . 18 1.3 R-parity Violating Supersymmetry . . . . . . . . . . . . . . . . . . . . . . 21 1.3.1 Sparticle Pair Production . . . . . . . . . . . . . . . . . . . . . . . 23 1.3.2 Single Sparticle Production . . . . . . . . . . . . . . . . . . . . . . 24 1.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2 Monte Carlo Simulations 27 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.2 Hard Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.3 Parton Showers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.3.1 Collinear Parton Showers . . . . . . . . . . . . . . . . . . . . . . . . 34 2.3.2 Angular-ordered Parton Showers . . . . . . . . . . . . . . . . . . . 40 2.3.3 Monte Carlo Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.4 Hadronization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.5 Monte Carlo Event Generators . . . . . . . . . . . . . . . . . . . . . . . . . 54 2.6 Angular Ordering in R . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 p 6 2.6.1 Decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 2.6.2 Hard Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 2.7 Hadronization of R Processes . . . . . . . . . . . . . . . . . . . . . . . . . 66 p 6 2.8 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 2.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 i 3 Resonant Slepton Production in Hadron–Hadron Collisions 77 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.2 R Decays of the Resonant Slepton . . . . . . . . . . . . . . . . . . . . . . 78 p 6 3.3 Gauge Decays of the Resonant Slepton . . . . . . . . . . . . . . . . . . . . 82 3.3.1 Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 3.3.2 Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 3.3.3 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 3.3.4 Mass Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . 116 3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 4 KARMEN Anomaly 123 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 4.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 4.2.1 Pion Decay Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 4.2.2 Neutralino Lifetime . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 4.2.3 Solutions of the KARMEN Anomaly . . . . . . . . . . . . . . . . . 133 4.3 Limits on the R-parity Violating Couplings . . . . . . . . . . . . . . . . . . 133 4.4 Experimental Constraints on a Light Neutralino . . . . . . . . . . . . . . . 136 4.4.1 Bounds from e+e νν¯γ . . . . . . . . . . . . . . . . . . . . . . . 136 − → 4.4.2 Bounds from the Invisible Z Width . . . . . . . . . . . . . . . . . . 137 4.4.3 Solutions in the MSSM Parameter Space . . . . . . . . . . . . . . . 138 4.4.4 Limits from Precision Electroweak Measurements . . . . . . . . . . 139 4.5 Future Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 5 Conclusions 147 Addendum 148 A Feynman Rules and Conventions 151 A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 A.2 Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 A.2.1 Charginos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 A.2.2 Neutralinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 A.2.3 Left/Right Sfermion Mixing . . . . . . . . . . . . . . . . . . . . . . 157 A.3 Gaugino Interactions with the Sfermions . . . . . . . . . . . . . . . . . . . 158 A.4 Gluino Interactions with the Squarks . . . . . . . . . . . . . . . . . . . . . 163 A.5 Gauge Boson Interactions with the Sfermions and Fermions . . . . . . . . . 163 A.6 Higgs Boson Interactions with the Sfermions and Fermions . . . . . . . . . 168 A.7 R-parity Violating Feynman Rules . . . . . . . . . . . . . . . . . . . . . . . 174 B Decay Rate Calculations 179 B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 B.2 Sfermions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 B.3 Charginos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 B.4 Neutralinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 ii B.5 Gluinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 C Cross-section Calculations 191 C.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 C.2 LQD Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 C.2.1 Resonant Slepton Production followed by Weak Decay . . . . . . . 191 C.2.2 Resonant Slepton Production followed by R Decay . . . . . . . . . 193 p 6 C.2.3 Resonant Slepton Production followed by Higgs Decay . . . . . . . 193 C.3 UDD Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 C.3.1 Resonant Squark Production followed by Weak Decay . . . . . . . . 194 C.3.2 Resonant Squark Production followed by R Decay . . . . . . . . . 196 p 6 C.3.3 Resonant Squark Production followed by Higgs Decay . . . . . . . . 196 Bibliography 199 iii iv