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26 2.4. The RPR model: the good, the bad and the ugly1.0Regge1.0Regge + resonancesχ 210 20.50.510cosθ K*0.00.010.50.510 11.02000 25001.0(MeV)W KY2000 250010 2Figure 2.8 – The performance of the Regge (left panel) and RPR (right panel) model for the descriptionof the p(γ, K + )Λ data. Every data point represents a (W KY , θK ∗ ) vector. The colour code indicates the χ2of the model for a particular data point. Data from Refs.[119–123, 125, 132, 140–142].1.0Regge1.0Regge + resonancesχ 210 20.50.510cosθ K*0.00.010.50.510 11.02000 25001.0(MeV)W KY2000 250010 2Figure 2.9 – The performance of the Regge-3 (left panel) and RPR-3 (right panel) model for the descriptionof the p(γ, K + )Σ 0 data. Every data point represents a (W KY , θK ∗ ) vector. The colour code indicates theχ 2 of the model for a particular data point. Data from Refs.[119–122, 125, 130, 134, 135, 140].reaction channels. This is an indication of the data inconsistencies alluded to in Ref. [131].Over the full energy range the RPR model nicely reproduces the data at forward angles. We remindthe reader that only the cos θK ∗ ≥ 0.35 data were included in the fits. In Figures 2.6 and 2.7,this region is indicated with a vertical band. At backward angles, on the other hand, the RPRpredictions feature bumps that are absent in the data. These structures occur near threshold forK + Σ 0 production and are prominent at higher energies in the p(γ, K + )Λ channel. The difficulty ofthe RPR model to account for the data in the backward hemisphere is readily visualised in Figures 2.8and 2.9. They show the χ 2 for the Regge and RPR models per data point, that is cross sections aswell as polarisation observables.The RPR-model analysis of Refs. [39, 40, 97] was limited to forward angles, motivated by theRegge model’s region of validity. At backward angles, one could expect that meson production canbe parametrised with Reggeized hyperon exchange in the u-channel [112]. Such an approach haspreviously been applied in pion photoproduction [38]. For kaon production, however, the cross-sectiondata shown in Figures 2.6 and 2.7 lack of any form of peaking at backward angles. This rules outthe need for a Regge approach. We judge that the inclusion of nucleon resonances in the s-channelcan account for strangeness production over the full solid angle. Therefore, the restriction on theangular range of the data used in the fitting database is relieved in the forthcoming RPR-modelanalysis [98, 133]. This allows for a successful description of kaon production at all angles.
Chapter 2. The Regge-plus-resonance formalism 27C xC z1.51.00.50.00.51.01.51.00.50.00.51.01.51.51.00.50.00.5*cosθ = 0.751.0 *Kcosθ = 0.251.0 *Kcosθ K= 0.851800 2000 2200 24001.52600 1800 2000 2200 24001.52600 1800 2000 2200 2400 26001.01.00.50.00.5*cosθ = 0.751.0 *Kcosθ = 0.251.0 *Kcosθ K= 0.851800 2000 22001.52400 2600 1800 2000 22001.52400 2600 1800 2000 2200 2400 2600(MeV)W KY1.51.00.50.00.50.50.00.5ReggeRegge + resonancesFigure 2.10 – Beam-recoil polarisation asymmetries C x (upper panels) and C z (lower panels) for thep(γ, K + )Λ reaction as function of the kaon-hyperon invariant mass W KY at three kaon scattering angles.The solid and dashed curves are calculations with the RPR and Regge models respectively. Data fromRef. [140].Despite its shortcomings, the RPR model provides an efficient description of EM kaon production.This is exemplified by the excellent predictions for the beam-recoil polarisation asymmetries (2.23).In Figure 2.10, the observables C x and C z are displayed at forward and backward angles. Theseasymmetries have the remarkable feature that at nearly all kinematics C x remains close to zero andthat C z is near its upper limit +1. The Regge model reproduces these gross features. The additionof s-channel resonances further improves the model’s correspondence with the data. Given that theresults of Figure 2.10 are predictions, this illustrates the predictive power of the RPR formalism.Figure 2.11 features the beam-recoil asymmetries obtained with linearly polarised photons. TheRPR models fails to reproduce the data near threshold, where the resonances provide marginalcontributions. Since the lowest-mass resonance considered in the RPR-model analysis is the S 11 (1650),this might point at the need to consider sub-threshold resonances. At the higher energy bins, thepredicted role of the resonances grows and their inclusion greatly improves the agreement with thedata.The extension of the RPR formalism to kaon electroproduction does not require any additionalparameters. The electroproduction results are thus pure predictions. Nevertheless, an adequatedescription of the data is achieved [69, 97]. Here, we simply wish to illustrate this using tworecently published data sets. In Ref. [143], new results for the separated longitudinal and transversep(e, e ′ K + )Λ cross sections are presented. They are compared to predictions from the Saclay-Lyonisobar model [22] and a Regge model [144] that resembles the one presented in Section 2.2. Weshow the new data in Figure 2.12. It is clear the Regge model underpredicts σ T , but exhibits theobserved flat energy dependence. The longitudinal cross section is well described at Q 2 = 1.90 GeV 2 .At the highest Q 2 bin, however, the predicted cross section lies below the data. The authors ofRef. [143] mention that the general EM kaon form factor is off shell when used in a t-channel diagram.Therefore, it becomes function of the momentum transfer t in addition to the photon’s virtuality Q 2 .In order to better describe the observed energy dependence with the Regge model, they introduce
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 35: 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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