Durham E-Theses Supersymmetric model building with Dirac gauginos BUSBRIDGE, DANIEL,WILLIAM How to cite: BUSBRIDGE, DANIEL,WILLIAM (2015) Supersymmetric model building with Dirac gauginos, Durham theses, Durham University. Available at Durham E-Theses Online: http://etheses.dur.ac.uk/11108/ Use policy The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the metadata record in Durham E-Theses • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders. Please consult the full Durham E-Theses policy for further details. Academic Support Oce, Durham University, University Oce, Old Elvet, Durham DH1 3HP e-mail: [email protected] Tel: +44 0191 334 6107 http://etheses.dur.ac.uk Supersymmetric model building with Dirac gauginos Daniel William Busbridge A Thesis presented for the degree of Doctor of Philosophy Institute for Particle Physics Phenomenology Department of Physics University of Durham England September 2014 To my parents Ray and Diane Busbridge for their endless support and encouragement Supersymmetric model building with Dirac gauginos Daniel William Busbridge Submitted for the degree of Doctor of Philosophy September 2014 Abstract With the Large Hadron Collider about to start its second run, we are in an era of high{energy collider physics. The discovery of a Standard Model{like Higgs boson with a mass of 125 GeV is a fantastic achievement, but the non{observation of supersymmetry (or any other mechanism of choice that stabilises the electroweak scale) is a tantalising puzzle. In this work, we investigate the possibility that a particular non{minimal reali- sation of supersymmetry | one with Dirac gauginos | can be a reasonably natural way of explaining this nonobservation, but can still can stabilise electroweak physics. We construct a simple UV completion of a model with Dirac gluinos dubbed Con- strained Dirac gluino mediation and determine the characteristic low energy spectra, the production cross sections of key processes at the Large Hadron Collider and the degree of fine tuning for a representative range of parameters. Noting that theories with Dirac gluinos have a tendency to lose asymptotic freedom due to the presence of extra matter content, we then cast our eyes towards Seiberg Duality and its gener- alisation to include adjoint chiral superfields | Kutasov duality and investigate how a Dirac mass maps across this duality. We provide evidence that a Dirac gaugino mass maps between electric and magnetic Kutasov descriptions as m m~ lim D ! lim D !1 1 ! 1 µ g κ k+1 µ 0 g~ κ~ k+1 using renormalisation group arguments and harmonic superspace techniques. Declaration The work in this thesis is based on research carried out at the Institute for Particle Physics Phenomenology, the Department of Physics, Durham University, England. No part of this thesis has been submitted elsewhere for any other degree or quali- fication. The research described in this thesis, unless referenced to the contrary in the text, has been carried out in collaboration with Valya Khoze and Steven Abel. Chapter 4 is based on the (to be) published work [1]: Daniel Busbridge Constrained Dirac gluino mediation arXiv:1408.4605 Chapter 5 is based on the published work [2]: Steven Abel and Daniel Busbridge Mapping Dirac gaugino masses Journal of High Energy Physics (June, 2013) 37 arXiv:1306.6323 Copyright ⃝c 2014 by Daniel William Busbridge. \The copyright of this thesis rests with the author. No quotations from it should be published without the author's prior written consent and information derived from it should be acknowledged". iv Acknowledgements There are a number of people who have been a great help to me during the creation of this work; for academic reasons, for maintaining my sanity or in many cases both: • My supervisor, Valya Khoze, for his invaluable guidance and useful discussions, for incredible patience and for giving me the opportunity to investigate so many different areas of theoretical particle physics; • My collaborator, Steve Abel, for our many enlightening discussions and for all that he taught me, both of a physics nature and of the realities of research; • J¨orgJ¨ackel and C´elineBœhm for their thorough (but enjoyable) examination of this thesis and the resulting amendments; • Alberto Mariotti for helpful conversations and Mark Goodsell, Florian Lyonnet and Florian Staub for useful correspondence; • All of my friends at the IPPP, both past and present, for generally being great. In particular I would like to thank my fellow OC118 office mates | Darren, Herr Yip, Jon, Malte, Mark, Oli, Peter, Ryan and Tom | for their shared appreciation of plush animals, enthusiasm for question of the day, and general surreality. I hope the OC118 (and friends) fine dining consortium continues its well established tradition, and that the latt´eadventure lives on; • Mike Johnson, Ewan Steele and Oliver Smith for all things IT, and Linda Wilkinson and Trudy Forster for all things logistic; • My housemates for the last two years, Andy and James, for their support, encouragement, and excellent cooking; v vi • The friends I've met through Hatfield College | particularly Alex, Hanna, Henry, Jack, Philippa, Tish and Zoe | for their indispensable help of a non{ physics variety, and Anthony Bash, whose advice, support and excellent con- versations over breakfast will be missed; • The Science and Technology Facilities Council for funding my studies; • All of my family, particularly my parents, my sister and my grandmother, for being an endless supply of encouragement over the years. February 19, 2015 Contents Abstract iii Declaration iv Acknowledgements v 1 Introduction 1 1.1 Non{technical overview . 1 1.2 Outline of thesis . 4 2 Foundations 6 2.1 The Standard Model of particle physics . 6 2.1.1 Introduction . 6 2.1.2 The Gauge Hierarchy Problem . 17 2.2 Effective field theories, schemes and the decoupling theorem . 21 2.3 Supersymmetry . 24 2.3.1 Basics . 24 2.3.2 Motivation . 27 2.3.3 Writing an N = 1 supersymmetric theory . 28 2.3.4 Writing a theory with extended supersymmetry . 39 2.3.5 R symmetry . 49 2.3.6 The holomorphic basis and non-renormalisation . 50 2.3.7 Supersymmetry breaking . 55 2.3.8 Dualities and mapping soft terms . 59 2.3.9 The Minimal Supersymmetric Standard Model . 71 2.3.10 Naturalness in trouble . 75 vii Contents viii 3 Dirac gauginos 79 3.1 Introduction . 79 3.2 Dirac versus Majorana particles . 81 3.2.1 Continuous symmetries . 81 3.2.2 Propagators . 83 3.3 Can gauginos be Dirac? . 85 3.3.1 Requirements . 85 3.3.2 Right handed degree of freedom . 85 3.3.3 R symmetry . 88 3.3.4 Origins from extended supersymmetry . 88 3.4 Supersoftness . 90 3.5 Supersafeness . 94 3.6 The MSSM with Dirac gauginos . 100 3.6.1 General superpotential and soft terms . 100 3.6.2 Electroweakino masses . 103 3.6.3 Higgs sector Electroweak symmetry breaking . 103 3.6.4 The (T)NMSSM effect . 110 3.6.5 The rho parameter and custodial symmetry breaking . 112 3.6.6 Tachyons . 114 3.6.7 Higgs quartic coupling suppression . 118 4 Constrained Dirac gluino mediation 124 4.1 Overview . 124 4.2 Generating a gluino mass . 125 4.3 Constrained Dirac gluino mediation . 126 4.3.1 Overview . 126 4.3.2 Boundary conditions at the Messenger scale . 127 4.3.3 One loop thresholds at the Dirac gluino mass . 131 4.4 Numerical setup . 133 4.5 Spectra . 134 4.5.1 Constrained General Gauge Mediation . 142 4.5.2 Overview . 145 4.6 Cross sections . 146 4.7 Decays of the pseudosgluon . 149 February 19, 2015 Contents ix 4.8 EWSB and fine tuning . 157 4.9 Chapter summary . 161 5 Mapping Dirac gaugino masses 163 5.1 Background and purpose . 163 5.2 Introduction . 164 5.3 A key observation . 167 5.4 Overview of method . 168 5.5 From Kutasov duality to N = 2 duality . 169 5.5.1 No flowing between fixed points and fixed lines . 170 5.5.2 Perturbative flow to N = 2 SQCD via Kutasov theory . 173 5.5.3 Higgsing in the dual theory and flow to N = 2 SQCD0 .... 174 5.5.4 Flow away from Nf = 2 Nc .................... 178 5.6 N = 2 !N = 1 with a superpotential for X .............. 179 5.6.1 Overview . 179 5.6.2 N = 2 SU(Nc) SQCD . 179 5.6.3 N = 2 !N = 1 SU(Nc) SQCD . 180 5.7 N = 2 !N = 0 with gaugino masses . 191 5.7.1 Overview . 191 5.7.2 How to add a Dirac gaugino mass . 191 5.8 Duality relations for the broken theory . 194 5.8.1 N = 1 couplings and gaugino masses . 194 5.8.2 A note on quarks under electric{magnetic duality . 197 5.9 Chapter summary . 198 Appendix 199 A One loop scalar integrals 200 B Additional plots for CDGM 202 B.1 The Constrained MSSM . 202 B.2 Constrained General Gauge Mediation . 206 C RGEs with Dirac gluino decoupling 218 C.1 Method and notation . 218 February 19, 2015 Contents x C.2 Renormalisation group equations . 219 C.2.1 SUSY parameters . 219 C.2.2 SUSY breaking parameters . 220 D Numerically solved perturbative flows to N = 2 SQCD 230 E Harmonic superspace and N = 2 SQCD 231 E.1 Integration rules for harmonic functions .