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Table of Contents
Supervisor's Foreword; Abstract; Acknowledgements; Contents; 1 Introduction; 1.1 Introduction; References; 2 Chiral EW Lagrangian; 2.1 Equivalence Theorem; 2.2 The Chiral Lagrangian and Its Parameterizations; 2.2.1 WBGB Scattering; 2.2.2 Coupling with gg; 2.2.3 Coupling with tt; References; 3 Scattering Amplitudes; 3.1 Generic form of the WBGB Scattering Amplitude and the Isospin Basis; 3.1.1 Decomposition of Elastic Scattering ww to ww; 3.1.2 Higgs
Higgs Cross-Channel: ww to hh and hh to hh Amplitudes; 3.1.3 Other Channels: wz to wz
3.2 LO and NLO Computation of Invariant Scattering Amplitudes3.2.1 ww Scattering; 3.2.2 2gamma Scattering; 3.2.3 tt in the Final State; 3.2.4 tt->tt Scattering Amplitude; 3.3 Partial Wave Decomposition; 3.3.1 ww Scattering; 3.3.2 gg Scattering Into and Out of the EWSBS; 3.3.3 tt in the Final State; 3.3.4 Validity Range of the Approximations; References; 4 Analytical Properties and Unitarization; 4.1 Unitarity Condition for Partial Waves; 4.2 Poles on the Analytical Continuation; 4.2.1 Spurious Resonances; 4.2.2 Numerical Search for Poles on the s-plane
4.3 Unitarization Procedures for ww Scattering4.3.1 Dispersion Relations; 4.3.2 Inverse Amplitude Method; 4.3.3 N/D Method; 4.3.4 K-matrix and Improved K-matrix; 4.3.5 Summary of the Unitarization Methods and Their Range of Applicability; 4.4 Extensions of the ww Unitarization; 4.4.1 gg Scattering Without hh Channel (a2=b), J=0; 4.4.2 gg Scattering with hh Channel, J=0; 4.4.3 gg Scattering Without hh Channel (a2=b), J=2; 4.4.4 gg Scattering with hh Channel, J=2; 4.4.5 tt in the Final State Without hh Channel (a2=b), J=0; 4.4.6 tt in the Final State with hh Channel, J=0; References
B.2 Analysis of the Spinors of the tt->tt ProcessAppendix C Dimensional Regularization and Passarino
Veltman Functions; Appendix D Several Proofs and Explanations; D.1 Integral over the Surface of a D-Dimensional Sphere; D.2 Integration of Legendre Polynomials; D.3 Integrals for the N/D Method; D.4 Comparison of Our Elastic ww Partial Waves with a Higgsless ECL Model; D.5 Concerns About the Applicability Conditions of the ET; Appendix E Feynman Diagrams for the Effective Lagrangian; E.1 ww Scattering, Isospin Basis, LO Coefficients; E.2 ww Scattering, Isospin Basis, NLO Coefficients
Higgs Cross-Channel: ww to hh and hh to hh Amplitudes; 3.1.3 Other Channels: wz to wz
3.2 LO and NLO Computation of Invariant Scattering Amplitudes3.2.1 ww Scattering; 3.2.2 2gamma Scattering; 3.2.3 tt in the Final State; 3.2.4 tt->tt Scattering Amplitude; 3.3 Partial Wave Decomposition; 3.3.1 ww Scattering; 3.3.2 gg Scattering Into and Out of the EWSBS; 3.3.3 tt in the Final State; 3.3.4 Validity Range of the Approximations; References; 4 Analytical Properties and Unitarization; 4.1 Unitarity Condition for Partial Waves; 4.2 Poles on the Analytical Continuation; 4.2.1 Spurious Resonances; 4.2.2 Numerical Search for Poles on the s-plane
4.3 Unitarization Procedures for ww Scattering4.3.1 Dispersion Relations; 4.3.2 Inverse Amplitude Method; 4.3.3 N/D Method; 4.3.4 K-matrix and Improved K-matrix; 4.3.5 Summary of the Unitarization Methods and Their Range of Applicability; 4.4 Extensions of the ww Unitarization; 4.4.1 gg Scattering Without hh Channel (a2=b), J=0; 4.4.2 gg Scattering with hh Channel, J=0; 4.4.3 gg Scattering Without hh Channel (a2=b), J=2; 4.4.4 gg Scattering with hh Channel, J=2; 4.4.5 tt in the Final State Without hh Channel (a2=b), J=0; 4.4.6 tt in the Final State with hh Channel, J=0; References
B.2 Analysis of the Spinors of the tt->tt ProcessAppendix C Dimensional Regularization and Passarino
Veltman Functions; Appendix D Several Proofs and Explanations; D.1 Integral over the Surface of a D-Dimensional Sphere; D.2 Integration of Legendre Polynomials; D.3 Integrals for the N/D Method; D.4 Comparison of Our Elastic ww Partial Waves with a Higgsless ECL Model; D.5 Concerns About the Applicability Conditions of the ET; Appendix E Feynman Diagrams for the Effective Lagrangian; E.1 ww Scattering, Isospin Basis, LO Coefficients; E.2 ww Scattering, Isospin Basis, NLO Coefficients