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24 2.4. The RPR model: the good, the bad and the ugly0.50.4E γ= 1125 MeV0.50.4E γ= 1275 MeV0.50.4E γ= 1425 MeV0.30.30.30.20.20.20.10.10.10.50.51.0 0.5 0.0 0.5 1.0E γ = 1575 MeV0.40.4E γ0.50.5 0.0 0.5 1.0= 1725 MeV0.4E γ0.5 0.0 0.5 1.0= 1875 MeV0.30.20.30.20.30.2dσ/dΩ (µb/sr)0.10.10.50.51.0 0.5 0.0 0.5 1.0E γ = 2025 MeV0.40.4E γ0.10.50.5 0.0 0.5 1.0= 2175 MeV0.4E γ0.5 0.0 0.5 1.0= 2325 MeV0.30.20.10.30.20.10.30.20.10.50.51.0 0.5 0.0 0.5 1.0E γ = 2475 MeV0.40.40.30.30.20.2E γ0.50.5 0.0 0.5 1.0= 2625 MeV0.40.30.2E γ0.5 0.0 0.5 1.0= 2775 MeVReggeRegge + resonances0.10.10.10.00.01.0 0.5 0.0 0.5 1.00.5 0.0 0.50.01.0*cosθ K0.5 0.0 0.5 1.0Figure 2.6 – Differential p(γ, K + )Λ cross sections as a function of θ ∗ K for various photon energies E γ. Thesolid and dashed curves are calculations with the RPR and Regge models respectively. The vertical bandshows the angular range used for fitting. Data from Refs. [119] (•), [125] (), [132] () and [123] (□).the newest CLAS results and the older data sets. This implies the Regge model can be furtherrefined. The repercussions for the RPR model are thoroughly addressed in Ref. [98].In order to keep the model uncertainties to a strict minimum and maintain a low number of fittingparameters, resonances of spin-5/2 and higher are not considered in Refs. [39, 40]. The RPP lists anumber of well-established higher-spin resonances that are indispensable in the description of (double-)pion production amongst others. Previous strangeness-production models that have consideredspin-5/2 resonance exchange [5, 22, 24, 29, 128], on the other hand, conclude that these states do notcontribute significantly to the reaction dynamics. Nevertheless, the forthcoming analysis [98, 133] ofthe recent kaon-production data in the RPR approach takes spin-5/2 resonances into account.Implementing resonances with spin J ≥ 3/2 in a hadrodynamical framework is a non-trivial task.The conventional Rarita-Schwinger description of high-spin fermion fields [136], which is adopted inthis work, involves some unphysical degrees of freedom, associated with their lower-spin content [137].These degrees of freedom are manifested by the off-shell parameters (X, Y, Z) that feature in the
Chapter 2. The Regge-plus-resonance formalism 250.50.4E γ= 1125 MeV0.50.4E γ= 1275 MeV0.50.4E γ= 1425 MeV0.30.30.30.20.20.20.10.10.10.50.51.0 0.5 0.0 0.5 1.0E γ = 1575 MeV0.40.4E γ0.50.5 0.0 0.5 1.0= 1725 MeV0.4E γ0.5 0.0 0.5 1.0= 1875 MeV0.30.20.30.20.30.2dσ/dΩ (µb/sr)0.10.10.50.51.0 0.5 0.0 0.5 1.0E γ = 2025 MeV0.40.4E γ0.10.50.5 0.0 0.5 1.0= 2175 MeV0.4E γ0.5 0.0 0.5 1.0= 2325 MeV0.30.20.10.30.20.10.30.20.10.50.51.0 0.5 0.0 0.5 1.0E γ = 2475 MeV0.40.40.30.30.20.2E γ0.50.5 0.0 0.5 1.0= 2625 MeV0.40.30.2E γ0.5 0.0 0.5 1.0= 2775 MeVReggeRegge + resonances0.10.10.10.00.01.0 0.5 0.0 0.5 1.00.5 0.0 0.50.01.0*cosθ K0.5 0.0 0.5 1.0Figure 2.7 – Differential p(γ, K + )Σ 0 cross sections as a function of θ ∗ K for various photon energies E γ.The solid and dashed curves are calculations with the RPR-3 and Regge-3 models respectively. The verticalband shows the angular range used for fitting. Data from Refs. [121] (•), [119] (), [134] (), [135] (),[125] (◦) and [130] (□).interaction Lagrangians (see Section D.3) and give rise to unphysical structures in the transitionamplitude [138]. Extending the work of Pascalutsa [139], a consistent interaction theory for high-spinfermions was formulated in Ref. [99]. In the forthcoming RPR model [98, 133], these consistentinteraction Lagrangians will be adopted for spin-3/2 and spin-5/2 resonance exchange.As mentioned in Section 2.3, the RPR-model analysis of Refs. [39, 40] was restricted to forward kaonproductionangles. Later on in this work, the RPR elementary-production operator will constituteone of the basic ingredients of the strangeness-production calculations from the deuteron. To this end,we wish to assess the behaviour of the RPR model over the full angular range. In Figures 2.6 and 2.7,the p(γ, K + )Λ and p(γ, K + )Σ 0 differential cross sections are shown for 1125 ≤ E γ ≤ 2775 MeV.Immediately, one notices that the Reggeized background model provides a fair description of thecross section even though it was optimised against high-energy data. In the threshold region, theRegge model overpredicts the Λ-production data, whereas it accounts for about half the strengthof the K + Σ 0 channel. At higher energies, the Regge model slightly overpredicts the data in both
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 and 18: Chapter 1. Introduction 7+ +Figure
Page 19 and 20: Chapter 1. Introduction 9are set ag
Page 21 and 22: CHAPTER 2The Regge-plus-resonance f
Page 23 and 24: Chapter 2. The Regge-plus-resonance
Page 33: Chapter 2. The Regge-plus-resonance
Page 41 and 42: CHAPTER 3Kaon production in data-po
Page 43 and 44: Chapter 3. Kaon production in data-
Page 65 and 66: CHAPTER 4Radiative kaon captureAfte
Page 67 and 68: Chapter 4. Radiative kaon capture 5
Page 69 and 70: Chapter 4. Radiative kaon capture 5
Page 71 and 72: CHAPTER 5Formalism for electromagne
Page 73 and 74: Chapter 5. Formalism for electromag
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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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