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8 Chapter 1. IntroductionRenard and Renard were among the pioneers to study kaon production on the nucleon and alsoled the way in strangeness reactions from the deuteron [77, 78]. In their work, they employeda simple parametrisation of the Y N interaction. Modern hyperon-nucleon potentials based onone-boson exchange were used in Refs. [73, 79, 80]. Yamamura et al. were the first to revisit thereaction adopting a modern elementary kaon-production operator optimised against high-qualitydata [81]. Including the effect of hyperon-nucleon FSI with the Nijmegen Y N potential, the inclusiveand exclusive charged-kaon-production cross sections were studied. At a later time, polarisationobservables in exclusive kaon photoproduction were investigated [82]. The approach was extended inRefs. [83, 84] to include two-step production and kaon-nucleon rescattering. Adopting this model,neutral-kaon photoproduction has been studied. Refs. [85, 86] have focused on the extraction of theelementary amplitude. A different study on the influence of Y N rescattering using the P -matrixapproach was presented in Ref. [87]. Maxwell considered a host of rescattering diagrams where a π,η or K meson is exchanged between the active nucleon, which absorbs the incoming photon, and thespectator nucleon [28, 88]. In Refs. [89, 90], kaon photoproduction from deuteron is investigated usinga variety of isobar models in the non-relativistic plane-wave impulse approximation, demonstratingthe importance of a reliable elementary-production operator. Gasparyan et al. studied the possibilityto extract the low-energy Λn scattering parameters [91]. They investigated specific polarisationobservables and kinematics needed to isolate the singlet and triplet states of Λn scattering. Likewise,Laget identifies well-defined regions in phase space where KN and Y N rescattering dominate whilethe elementary amplitude is on shell and the momentum of the spectator nucleon is low [92, 93]. Todate, very few studies have considered electron-induced strangeness production from the deuteron.Hsiao and Cotanch [94, 95] used the elementary-production operator of Thom [17]. In Ref. [96] theSaclay-Lyon model [22] was adopted.OutlineIn this work, we present a covariant formalism for the photo- and electroproduction of kaons andhyperons from the deuteron, thereby accounting for hyperon-nucleon rescattering.In Chapter 2, the elementary-production operator is introduced. We begin our discussion with anoverview of the kinematics and observables relevant to EM kaon production from the nucleon. Then,we turn our attention to the RPR formalism. At high-energies, an adequate description of the datais realised using the Regge model. The Reggeization procedure is discussed and an elegant recipeto guarantee a gauge-invariant amplitude is outlined. In a next step, a model including resonanceexchangediagrams is optimised to the resonance-region data, while the three free parameters ofthe Regge model are held fixed. Successful descriptions of the K + Λ- and K + Σ 0 -production dataobtained before 2007 are realised. We conclude this chapter with a critical discussion of the RPRmodel as it was published in Refs. [39, 40, 69, 97]. Recent developments of the RPR formalism arehighlighted and comparisons with the latest photo- and electroproduction results are shown. Thisillustrates the descriptive and predictive power of the RPR model in the data-rich reaction channels.Chapter 3 is devoted to those kaon-production channels where little or no experimental results areat hand. A formalism is presented in order to transform the RPR transition amplitude that wasfitted to p(γ (∗) , K + )Λ and p(γ (∗) , K + )Σ 0 to the other N(γ (∗) , K)Y reaction channels. At the stronginteractionvertices, one can rely on SU(2) isospin symmetry. The conversion of the EM couplingconstants, on the other hand, requires experimental input. The resulting RPR-model predictions
Chapter 1. Introduction 9are set against the world data for K + Σ − production from the neutron and K 0 Σ + production fromthe proton. The sensitivity to the errors bars of the applied photocoupling helicity amplitudes isinvestigated.In Chapter 4, we make a small digression. The Regge model is employed in a exploratory study ofnew results on radiative kaon capture. This reaction is related to kaon photoproduction throughcrossing symmetry and is sensitive to the excited states of Λ and Σ hyperons.After having established the RPR framework, we turn our attention to strangeness production fromthe deuteron in Chapter 5. The kinematics are reviewed and the observables of the reaction aredefined in terms of the transition amplitude. The deuteron wave function is an essential ingredient ofthe reaction dynamics and is discussed at length. We examine relativistic and non-relativistic wavefunctions and introduce a covariant vertex operator for the deuteron-neutron-proton transition. Thetransition amplitude is given in the relativistic impulse approximation. We define the plane-waveapproximation and provide a non-relativistic reduction. In addition, the contribution of hyperonnucleonrescattering is derived. We find that it can be decomposed in two parts. The first term hasall rescattering particles on mass shell, while the other involves off-mass-shell particles and allows forsub-threshold production.Chapter 6 is dedicated to the numerical results of the calculations. In a first step, the relativistic planewaveimpulse approximation is thoroughly investigated. We study the sensitivity of the computedobservables to relativistic effects, to the deuteron wave function, and to the off-shell extrapolation ofthe elementary-production operator. In addition, the propagation of the uncertainties related to kaonproduction from the neutron is investigated. Subsequently, the dynamics of the hyperon-nucleonrescattering contribution are examined. In the final section, we confront our predictions with theavailable experimental results. We state our conclusions in Chapter 7 and indicate directions forfuture work.For reasons of readability, many technical details have been diverted to the appendices. Appendix Aestablishes the notations and conventions assumed in this dissertation. In Appendix B, we brieflyintroduce the number system of biquaternions and their applicability as representation of the Lorentzgroup.Owing to their elegant transformation properties under Lorentz transformations, helicity spinors playan important role in our formalism. Appendix C is devoted to the subject. Appendix D summarisesthe rules and ingredients needed to compute cross sections. We list the interaction Lagrangiansadopted in this work, as well as the transition amplitudes for the Feynman diagrams considered inthe RPR model.In Appendix E, the derivation of two Lorentz-invariant forms of the 2 H(γ, KY )N cross section isgiven. The density-matrix formalism is the topic of Appendix F. Density matrices play an importantrole in the construction of polarisation observables.This work makes use of a number of deuteron wave functions. Their parametrisations are provided inAppendix G. Subsequently, Appendix H retraces the connection between these wave functions and thecovariant Dnp-vertex. In Appendix I, we tabulate the coupling constants of the adopted RPR modelfor all six strangeness-production reaction channels. An overview of the published experimental datafor kaon photoproduction from the nucleon is given in Appendix J. Lastly, Appendix K presentssome details about the hyperon-nucleon interaction and more specifically the Jülich potential.
Page 1: FACULTEIT WETENSCHAPPENRegge-plus-r
Page 6: viPrefaceUniversity, the Hercules F
Page 9 and 10: ContentsixD.3.2 Effective Lagrangia
Page 11 and 12: CHAPTER 1IntroductionConventional w
Page 13 and 14: Chapter 1. Introduction 3σ (µb)γ
Page 15 and 16: Chapter 1. Introduction 5meson-prod
Page 17: Chapter 1. Introduction 7+ +Figure
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Page 23 and 24: Chapter 2. The Regge-plus-resonance
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Chapter 4. Radiative kaon capture 5
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CHAPTER 5Formalism for electromagne
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Chapter 5. Formalism for electromag
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CHAPTER 6Results for kaon productio
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Chapter 6. Results for kaon product
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CHAPTER 7Conclusions and outlookMot
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Chapter 7. Conclusions and outlook
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APPENDIX ANotations and conventions
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Appendix A. Notations and conventio
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Appendix A. Notations and conventio
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APPENDIX BBiquaternionsAnd here the
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Appendix B. Biquaternions 125The bi
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APPENDIX CHelicity spinorsIn Sectio
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Appendix C. Helicity spinors 129whe
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APPENDIX DFeynman rulesIf I could e
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Appendix D. Feynman rules 133D.3.1P
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Appendix D. Feynman rules 135Born s
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APPENDIX ELorentz-invariant cross s
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Appendix E. Lorentz-invariant cross
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APPENDIX FDensity matrixScattering
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Appendix F. Density matrix 143The s
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Appendix F. Density matrix 145When
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APPENDIX GParametrisations of the d
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Appendix G. Parametrisations of the
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Appendix G. Parametrisations of the
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APPENDIX HConnecting (non-)relativi
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Chapter H. Connecting (non-)relativ
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APPENDIX IParameters of the Regge-p
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Chapter I. Parameters of the Regge-
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APPENDIX JExperimental dataFacts ar
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Chapter J. Experimental data 163Tab
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APPENDIX KHyperon-nucleon interacti
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Appendix K. Hyperon-nucleon interac
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Appendix K. Hyperon-nucleon interac
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SamenvattingNederlands is geen taal
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Samenvatting 173namelijk ondubbelzi
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Samenvatting 175de subtiele structu
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Samenvatting 177Productie van neutr
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Samenvatting 179off-shell-extrapola
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List of publicationsPart of the res
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BibliographyIf you steal from one a
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Bibliography 185[27] S. Janssen, J.
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Bibliography 187[58] D. G. Ireland,
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Bibliography 189[93] J. Laget, Pent
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Bibliography 191[127] M. Dugger et
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Bibliography 193http://www.jlab.org
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Bibliography 195[190] M. Galassi, J
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Bibliography 197[223] R. H. Dalitz,
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NomenclatureI strive to be brief, a
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Nomenclature 201r(⃗ω) Rotation t
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