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38 3.2. The unbound neutron as kaon-production target1= 2382 MeVW KY1= 2460 MeVW KY1= 2535 MeVW KY10 111dσ/dΩ (µb/sr)10 2Regge3Regge41.010.5 0.0 0.51= 2608 MeV1.010 1W KY21W KY0.5 0.0 0.51= 2679 MeV1.021W KY0.5= 2748 MeV0.0 0.5 1.010 2223101.0 0.5 0.0 0.5 1.030.5 0.0 0.5 1.0*cosθ K30.5 0.0 0.5 1.0Figure 3.4 – Regge-model predictions for the n(γ, K + )Σ − differential cross section as a function of θ K ∗for six different values of the kaon-hyperon invariant mass. Data from Ref. [151]. The error bars representthe total (statistical plus systematic) uncertainty.0.50.4WKY= 1745 MeV0.5Regge3Regge40.4= 1849 MeVW KY0.50.4= 1948 MeVW KY0.30.30.30.20.20.2dσ/dΩ (µb/sr)0.10.10.10.50.51.0W =0.52042 MeV0.0 0.5 1.0KY0.40.4W KY0.5= 2132 MeV0.0 0.50.51.00.4W KY0.5= 2219 MeV0.0 0.5 1.00.30.20.10.30.20.10.30.20.10.00.01.0 0.5 0.0 0.5 1.00.5 0.0 0.50.01.0*cosθ K0.5 0.0 0.5 1.0Figure 3.5 – Regge-model predictions for the n(γ, K + )Σ − differential cross section as a function of θ K ∗for six different values of the invariant mass W . Data from Ref. [151]. The error bars represent the total(statistical plus systematic) uncertainty.
Chapter 3. Kaon production in data-poor reaction channels 39differential cross section as a function of the scattering angle is characteristic for Regge-trajectoryexchange, and the Regge models naturally describe this trend. The magnitude at forward anglestends to be overpredicted however. In the backward hemisphere the experimental error bars aresubstantial. At these kinematics, the Regge-4 model predicts much larger cross sections compared tothe Regge-3 model. Overall, the calculations with the Regge-3 model agree better with the data.The angular dependence of the n(γ, K + )Σ − differential cross section obtained by the CLAS collaborationin the resonance region is shown in Figure 3.5. The quality of agreement of the Regge modelsis analogous to the situation with the LEPS results of Figure 3.2. The shape of the cross sectionis reproduced by the Regge-3 model, yet its strength is overestimated. Again, the data favour theRegge-3 model.In previous work [40, 97], we had not been able to discriminate between the two Regge models onthe basis of the p(γ (∗) , K + )Σ 0 data. In the n(γ, K + )Σ − channel, on the other hand, the Regge-3model clearly outperforms the Regge-4 variant. Accordingly, we will discard the latter from nowon. This implies that, for the remainder of this dissertation, we have two unique kaon-productionmodels at our disposal. For the Λ-production channels that is the Regge-2 and RPR-2 model. TheΣ-production reactions will be described using the Regge-3 and RPR-3 models.Both the differential cross section and the photon-beam asymmetry in Figures 3.2, 3.3 and 3.5 exhibita rather smooth energy dependence. The Regge model predictions procure a fair description, yetdiscrepancies exist. These can possibly be attributed to nucleon and ∆ resonances. Their role in then(γ, K + )Σ − reaction can be evaluated with the RPR amplitude. As was outlined in Paragraph 3.2.2,the transformation of the p(γ, K + )Σ 0 amplitude requires a set of helicity amplitudes. The valuesextracted in the latest SAID analysis, SP09 [127], are ill-suited for our purposes, as this analysisdoes not provide resonance couplings to neutrons. We performed calculations with the two other sets(RPP and SM95), and found them to produce qualitatively similar results. In what follows, we willdiscuss the representative results obtained with the helicity amplitudes extracted in the SAID SM95analysis [149]. No experimental information is available for the P 13 (1900) resonance. Therefore, weallow the ratios of its magnetic transition moments κ (1,2)N ∗ n /κ(1,2) N ∗ p(see Eqs. (3.13) and (3.14)) to varybetween −2 and +2. This range encompasses the Bonn model predictions. Since the EM transitionstrengths for delta resonances to protons and neutrons are identical, we include the D 33 (1700),S 31 (1900), P 31 (1910), and P 33 (1920) resonances with the EM coupling constants determined in thep(γ, K + )Σ 0 reaction channel.The amplitudes of the RPR-3 model are the sum of the Regge-3 background and resonance contributions.In Figures 3.6 and 3.7, we confront the RPR-3 and Regge-3 predictions for n(γ, K + )Σ − withthe LEPS data. One observes a destructive interference between the Reggeized background and theresonance diagrams. This reduces the reaction strength and marginally improves the agreement withthe cross section data in all angular bins and for all energies. From Figure 3.7, it is plain that theRegge-3 and RPR-3 models provide similar predictions for the photon-beam asymmetry Σ. Thisobservation leads us to conclude that the Σ observable is rather insensitive to resonance-exchangecontributions.From Table 3.1, we learn that the helicity amplitudes extracted in the SM95 analysis have considerableerror bars. Their impact is assessed in Figures 3.6 and 3.7, and is quite dramatic. Using the error barsgiven in table 3.1, we considered 21 equidistant values for every κ N ∗ nκand computed the n(γ, K + )Σ −N ∗ pobservables for each of these 21 6 combinations. The shaded area of Figures 3.6 and 3.7 indicates 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 47: 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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