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36 3.2. The unbound neutron as kaon-production targetdσ/dΩ (µb/sr)0.60.50.40.30.20.10.60.50.40.30.20.10.0*cosθ K= 0.651800 * 2000 2200cosθ K= 0.851800 2000 22000.60.50.40.30.20.10.60.50.40.30.20.1W KY*cosθ K= 0.751800*2000 2200cosθ K= 0.95 Regge3Regge40.01800 2000 2200(MeV)Figure 3.2 – Regge-model predictions for the n(γ, K + )Σ − differential cross section as a function of thekaon-hyperon invariant mass for four different values of the kaon centre-of-mass scattering angle. Datafrom Ref. [134]. The error bars represent the statistical uncertainties only. The systematic uncertainty is ofthe order of 20%.SAID analyses [127, 149]. It is clear that the photon couplings of those resonances pertinent to ourcalculations are poorly determined. The extracted values are often incompatible, even after takinginto account the considerable error bars. No experimental information is available for the resonances ofmass 1900 MeV, i.e. P 13 (1900) and D 13 (1900). Table 3.1 also features photon couplings as calculatedin the Bonn CQM [148]. The theoretical predictions for the transition moments of the S 11 (1650)to neutron (proton) agree favourably with the SAID analysis SM95 [149] (SP09 [127]). Whenconfronting the Bonn model calculations for the P 11 (1710) and P 13 (1720) resonances with the SM95SAID analysis, one notices that the transition moments to proton and neutron are overestimated,while their ratio matches within the error. The Bonn CQM provides a fair account of all A p J fromthe SP09 analysis. This analysis, however, finds no evidence for the P 11 (1710) resonance [150].3.2.3 ResultsIn Chapter 2, it became clear that the kaon-production reaction mechanism is dominated by thebackground contributions, which we parametrise in terms of Regge-trajectory exchange. Therefore,we will first examine the predictive power of the Reggeized-background model using the limitednumber of available experimental results. At a later stage, the predictions of the full RPR modelwill be investigated.To our knowledge, only two data sets for the n(γ, K + )Σ − reaction channel have been published inthe past. The results by the LEPS collaboration [134] comprise differential cross sections and photonbeamasymmetries at forward angles (cos θ ∗ K ≥ 0.65) in the energy range 1.5 GeV ≤ E γ ≤ 2.4 GeV.This data set has been obtained through quasi-free kaon photoproduction from a deuterium target.Systematic errors originate from corrections for final-state interactions, the pion-mediated two-stepprocess, and detector uncertainties. Quadratically summing the estimates given in Ref. [134] yieldsuncertainties of the order of 20 % for the differential cross section and |∆Σ| ≈ 0.2 for the photon-beam
Chapter 3. Kaon production in data-poor reaction channels 37Photonbeam asymmetry Σ1.51.00.50.00.51.51.00.50.00.51.0cosθ K= 0.650.51800 2000 2200*1.51.00.50.01.51.00.50.0cosθ K= 0.751800 2000 2200Regge3*cosθ = 0.850.5*KcosθRegge4K= 0.951.01800 2000 2200 1800 2000 2200(MeV)W KY*Figure 3.3 – Regge-model predictions for the n(γ, K + )Σ − photon-beam asymmetry as a function of thekaon-hyperon invariant mass for four different values of the kaon centre-of-mass scattering angle. Datafrom Ref. [134]. The error bars represent the statistical uncertainties only. The systematics are estimatedto be |∆Σ| ≈ 0.2.asymmetry.Figures 3.2 and 3.3 show our Regge-model predictions for the measured observables. The differentialcross section is fairly energy independent and settles between 0.1 and 0.2 µb. The predictions of theRegge models provide an acceptable description of the data. Overall, the quality of agreement isbetter for the Regge-3 variant. The Regge-4 model overpredicts the cross section by a factor of two,roughly. The LEPS data shows a clear predilection for the Regge-3 model.As can be appreciated from Figure 3.3, both Regge models provide a satisfactory account of thephoton-beam asymmetry, with a vanishing asymmetry at threshold and a steady rise as the energyincreases. Again, it should be stressed that these results do not involve any free parameters andare anchored to the fitted p(γ, K + )Σ 0 amplitude through SU(2) isospin symmetry at the stronginteraction vertex. Despite its simplicity, our approach can account quantitatively for the LEPSmeasurements.Recently, the CLAS collaboration made available a large set of n(γ, K + )Σ − differential-cross-sectionresults covering a broad angular range [151]. The data have been obtained using photons, in anenergy range from 0.8 GeV to 3.6 GeV, incident on a liquid-deuterium target. The photoproducedkaon and the pion and neutron coming from the decaying Σ − hyperon are detected. Subsequently, thepresence of the spectator proton is inferred by putting limits on the missing mass. In addition, a cuton the missing momentum |⃗p p | ≤ 250 MeV is applied. The systematic uncertainties are dominatedby the background subtraction and the photon-flux calculations, and are estimated to be about4.5–13.5%. Owing to the large energy coverage of the CLAS data, the dynamics of the n(γ, K + )Σ −reaction can be investigated in the resonance region and at higher energies.In Figure 3.4, Regge-model predictions are set against CLAS results at energies where the contributionof resonance exchange is judged to have died out. Clear peaks at forward scattering angles are visible.This indicates the dominance of K (∗) exchange in the t-channel. The exponential decrease of the
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 41 and 42: CHAPTER 3Kaon production in data-po
Page 43 and 44: Chapter 3. Kaon production in data-
Page 45: 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 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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