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4 Chapter 1. IntroductionFigure 1.2 – Tree-level contributions to the N(γ (∗) , K)Y amplitude. The ∆ ∗ -exchange term is forbiddenfor Λ production. The diagram in the bottom-left corner is resonant. The others are considered backgroundcontributions.interaction Lagrangians that reflect essential symmetry properties and conservation laws of theunderlying fundamental interaction. The finite spatial extension of the hadrons is incorporatedusing phenomenological form factors. Care has to be taken, because this procedure breaks the vitalproperty of gauge invariance [55].In the so-called isobar approach, the reaction dynamics are restricted to tree-level amplitudes,consisting of two interaction vertices and one propagator. The considered diagrams are presented inFigure 1.2 and can be classified according to several aspects. Considering the diagrams in Figure 1.2per column, we distinguish between the exchange of a non-strange baryon (N, N ∗ , ∆ ∗ ), a kaon (K)or a hyperon (Y , Y ∗ ), labelled s-, t- and u-channel respectively. The contributions in the top row areknown as Born terms and involve the exchange of a ground-state hadron (p, n, K, Λ, Σ). Finally, adiagram can be either resonant or non-resonant. In EM kaon production, the kinematical conditionsare such that the intermediary particle in the N ∗ - and ∆ ∗ -exchange amplitudes can be on mass shell.Consequently, the propagator goes through a pole and produces resonant structures in the observables.In the remaining diagrams of Figure 1.2, on the other hand, the exchanged particles cannot reachtheir resonant pole. As our interest in strangeness production is generated by the discovery potentialfor missing resonances, the contributions of the non-resonant diagrams are considered a background.Contrary to fundamental field theories, effective Lagrangians represent parametrisations of the mesonbaryoninteraction in terms of unknown coupling constants. A phenomenological analysis in the isobarapproach faces the challenge of determining the resonant content of a reaction while simultaneouslyfixing the unknown effective coupling strengths. This dual situation of model selection and modeloptimisation can be addressed via a Bayesian approach [56] at a substantial computational cost. Inany case, because the parameters of the resonant and background contributions are simultaneouslyfitted to the data, they are inevitably strongly correlated.The isobar framework has met with considerable success and has dominated the analysis of EM
Chapter 1. Introduction 5meson-production processes in the resonance region. Its application to strangeness-productionreactions should be regarded with caution. As seen in Figure 1.1, the total cross section lacksclear resonant structures, implying that resonant contributions do not dominate. For this reason,background diagrams make up a crucial element of the reaction dynamics. In the isobar approach,these non-resonant terms diverge as energy increases [57]. Over the years, several mechanisms toremedy this unrealistic behaviour have been proposed. The extracted resonance couplings, however,heavily depend on the background model [27, 58].The tree-level diagrams of Figure 1.2, considered in the isobar model, infer a perturbation serieswhich is truncated at lowest order. In practise, the effective coupling constants at the interactionvertices are by no means small, implying rescattering effects need to be taken into account. Numerousanalyses of kaon production have been performed in different CC frameworks. Nevertheless, we wishto stress the continued relevance of single-channel descriptions.An attractive quality of the CC approach is its natural fulfilment of unitarity. For this to hold true,however, all possible meson-baryon channels have to be considered. In view of the dominance of twopion-productionchannels in the photo-absorption process as seen in Figure 1.1, troublesome channelssuch as ππN, with the inherent three-body cut, cannot be circumvented. Since CC models involvenumerous reaction channels, the number of free parameters that need to be fitted is substantiallylarger than in single-channel approaches. Therefore, the task of optimising the model is far frombeing trivial. In addition, comparing the different γp → X reactions in Figure 1.1, one immediatelyobserves that the kaon-production channel is several orders of magnitude smaller than the dominantπN, ππN, and ρN final states. Due to the reduced size and quality of the strangeness-productiondatabase in comparison to these channels, constraining the model parameters to the kaon-productionresults is complicated.Because CC models still require tree-level amplitudes as input, many conceptual ambiguities relatedto the isobar approach remain relevant. Issues, such as the restoration of gauge invariance [55, 59, 60],continue to be pertinent [10] and can be more easily addressed at the level of a single-channel reactionmodel.The Regge model and beyondDespite the publication of a large body of high-quality p(γ (∗) , K)Y data in recent years, phenomenologicalanalyses have not led to an unequivocal outcome. Disentangling the relevant resonantcontributions is challenging, because of the large number of competing resonances above the kaonproduction threshold. Moreover, the smooth energy dependence of the measured observables hintsat a dominant role for the background, i.e. non-resonant, processes. Hence, the treatment of thebackground is pivotal for any model.At sufficiently high energies, the isobar description is no longer optimal. Whereas empirical informationindicates a smooth fall off for the cross section as one moves away from threshold, hadrodynamicalmodels reveal a pathological rise. It comes as no surprise that the use of hadronic degrees of freedomcannot be justified above centre-of-mass energies of a few GeV, which corresponds to length scalesbelow 0.1 fm. In this energy region, the kaon-production amplitude can be elegantly describedwithin the Regge framework, characterised by the exchange of whole families of particles, instead ofindividual hadrons [38]. The Regge formalism boasts a number of attractive properties. Its amplitude
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: Chapter 1. Introduction 3σ (µb)γ
Page 17 and 18: Chapter 1. Introduction 7+ +Figure
Page 19 and 20: Chapter 1. Introduction 9are set ag
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CHAPTER 4Radiative kaon captureAfte
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Chapter 4. Radiative kaon capture 5
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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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