List of Figures

1. The muon decay process
2. Schematic of jet formation via quark, anti-quark separation
3. Diagram of the accelerators at CERN.
4. Schematic representation of the OPAL detector
5. Detailed schematic of the OPAL cross-section
6. The trilinear gauge vertex
7. The two W-pair production processes which contain the trilinear gauge vertex
8. The t-channel single W production process which contains the trilinear gauge vertex
9. The t-channel W-pair production process
10. W-pair production cross-section as a function of centre-of-mass energy for the Standard Model
11. W-pair production cross-section as a function of centre-of-mass energy for a non-Standard Model case
12. The differential cross-section of W production at 189 GeV with CP-conserving anomalous couplings implemented
13. The differential cross-section of W production at 189 GeV with CP-violating anomalous couplings implemented
14. Production and decay angles of W bosons
15. Analytical prediction of the two-particle joint Spin Density Matrix elements
16. Single W Spin Density Matrix elements.
17. The analytical predictions for the individual W polarised differential cross-sections.
18. Analytical prediction for the imaginary parts of the single W Spin Density Matrix elements.
19. Angular distributions calculated from Standard Model Monte Carlo
20. Single W SDM elements calculated from Standard Model Monte Carlo
21. Two-particle joint W SDM elements calculated from Standard Model Monte Carlo
22. Polarised differential cross-sections calculated from Standard Model Monte Carlo.
23. CC03 Diagrams
24. CC10 Diagrams
25. CC20 Diagrams
26. NC24 Diagrams
27. NC48 Diagrams
28. ${\rm Z}^{0}/\gamma \rightarrow {\rm q}\bar{\rm q}$ processes
29. 2-photon process
30. Interfering QCD background
31. Outline of the organisation of the GOPAL program.
32. $\cos\theta_{\rm W}$ distributions for all and selected events only
33. True and reconstructed angular distributions for selected events
34. The angular distributions of the selected data events at 189 GeV
35. Single W SDM elements extracted from fully detector simulated Monte Carlo
36. Comparison of reweighted Monte Carlo to generated Monte Carlo
37. Comparison of the SDM elements extracted from reweighted Monte Carlo to those extracted from generated Monte Carlo
38. Bias plots of the CP-conserving TGCs fit using the WVCXME reweighting scheme
39. Bias plots of the CP-conserving TGCs fit using the BILGOU reweighting scheme
40. Bias plots of the CP-violating TGCs fit using the BILGOU reweighting scheme
41. Pull distributions for Standard Model Monte Carlo for the combined fit to the CP-conserving couplings using the BILGOU reweighting scheme
42. Pull distributions for Standard Model Monte Carlo for the combined fit to the CP-conserving couplings using the WVCXME reweighting scheme
43. Pull distributions for Standard Model Monte Carlo for the $\cos\theta_{\rm W}$fit to the CP-conserving couplings
44. Pull distributions for Standard Model Monte Carlo for the combined fit to the CP-violating couplings
45. Pull distributions for Standard Model Monte Carlo for the $\cos\theta_{\rm W}$fit to the CP-violating couplings
46. Single W SDM elements extracted from 189 GeV data
47. Normalised $\cos\theta_{\rm W}$ disribution extracted from the 189 GeV data
48. $\chi ^{2}$ plots of the fit of the CP-conserving couplings using the WVCXME reweighting scheme.
49. $\chi ^{2}$ plots of the fit of the CP-conserving couplings using the BILGOU reweighting scheme.
50. $\chi ^{2}$ plots of the fit of the CP-violating couplings using the BILGOU reweighting scheme.
51. $\chi ^{2}$ plots of the fit of the CP-conserving couplings, including systematic uncertainties, using the WVCXME reweighting scheme
52. $\chi ^{2}$ plots of the fit of the CP-conserving couplings, including systematic uncertainties, using the BILGOU reweighting scheme.
53. $\chi ^{2}$ plots of the fit of the CP-violating couplings, including systematic uncertainties, using the BILGOU reweighting scheme
54. Resolution of angular variables
55. Distribution of correction factors for $-0.25<$ $\cos\theta_{\rm W}$$<+0.0$
56. Distribution of correction factors for $0.75<$ $\cos\theta_{\rm W}$$<1.0$
57. Corrected single SDM elements from PYTHIA Monte Carlo
58. Corrected differential cross-sections calculated from PYTHIA Monte Carlo
59. The fraction of each polarisation state from Monte Carlo
60. Polarised cross-sections from Monte Carlo sub-sample.
61. Comparison of true and measured fractions of longitudinal W bosons from Monte Carlo sub-samples.
62. Comparison of true and measured fractions of each polarisation state from Monte Carlo sub-samples.
63. Measured fractions of polarised cross-sections from Monte Carlo sub-samples
64. Contribution to the polarised cross-sections from background events
65. Effect of background on normalised polarised differential cross-sections.
66. Individual W differential polarised cross-sections extracted from 189 GeV data
67. W-pair polarised cross-sections extracted from 189 GeV data
68. Single W SDM elements for generator modelling studies
69. Single W SDM elements for hadronisation studies
70. Model independent test of CP and CPT-violation
71. Plots of the final $\chi ^{2}$ fits for all TGCs
72. Bias plots of the CP-conserving TGCs fit using the BILGOU reweighting scheme
73. Bias plots of the CP-violating TGCs fit using the BILGOU reweighting scheme
74. Pull distributions for Standard Model Monte Carlo for the combined fit to the CP-conserving couplings using the BILGOU reweighting scheme
75. Pull distributions for Standard Model Monte Carlo for the combined fit to the CP-violating couplings
76. Plots of the final $\chi ^{2}$ fits for all TGCs
77. Plots of the final $\chi ^{2}$ fits for all TGCs