Compton Scattering Sum Rules for Massive Vector Bosons

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Autor: Jan Pieczkowski Theoretische Kernphysik Institut für Kernphysik Johannes-Gutenberg-Universität Mainz 55128 Mainz E-Mail: jan.pieczkowski@students.uni-mainz.de Betreuer: Prof. Dr. Marc Vanderhaeghen Dr. Vladimir Pascalutsa Theoretische Kernphysik Theoretische Kernphysik Institut für Kernphysik Institut für Kernphysik Johannes-Gutenberg-Universität Mainz 55128 Mainz 55128 Mainz E-Mail: marcvdh@kph.uni-mainz.de vladipas@kph.uni-mainz.de Zweitkorrektor: Apl.-Prof. Dr. Hubert Spiesberger Theoretische Hochenergiephysik Institut für Physik Johannes-Gutenberg-Universität Mainz 55128 Mainz E-Mail: hspiesb@mail.desy.de Diese Arbeit wurde mit Hilfe von KOMA-Script und L A TEX gesetzt.
Contents Introduction vii 1 Physical method 1 1.1 Introduction to Field Theory . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Gauge Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2.1 Internal Symmetries and Global Transformations . . . . . . . . 3 1.2.2 Local Invariance and Gauge Groups . . . . . . . . . . . . . . . . 5 1.2.3 Nonabelian Gauge Theory: Yang-Mills Theory . . . . . . . . . . 5 1.3 S-Matrix Formalism and Dispersion Theory . . . . . . . . . . . . . . . 6 1.3.1 Causality and Analyticity . . . . . . . . . . . . . . . . . . . . . 7 1.3.2 Dispersion Relations . . . . . . . . . . . . . . . . . . . . . . . . 9 2 Lagrangian Description of Charged Massive Vector Bosons 11 2.1 The Proca Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2 Charged Proca Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3 Construction of an Effective Lagrangian . . . . . . . . . . . . . . . . . 14 2.4 Gauge Invariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.5 Feynman Rules for L Eff . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.6 Electromagnetic Moments and Natural Values . . . . . . . . . . . . . . 20 3 Compton Scattering and Sum Rules 23 3.1 Decomposition of the Polarized Amplitude . . . . . . . . . . . . . . . . 24 3.1.1 Spin Algebra for Vector Particles . . . . . . . . . . . . . . . . . 24 3.1.2 Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.2 Scattering Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.3 Low-Energy Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.3.1 Original Theorem for Spin 1 /2 . . . . . . . . . . . . . . . . . . . 32 3.3.2 LET for Massive Vector Bosons . . . . . . . . . . . . . . . . . . 33 iii
Page 1: Compton Scattering Sum Rules for Ma
Page 5: Contents Acknowledgements 85 v
Page 8 and 9: Introduction Purpose of this Study
Page 10 and 11: Introduction Euclidian metric and s
Page 12 and 13: Chapter 1 Physical method the term
Page 14 and 15: Chapter 1 Physical method where the
Page 16 and 17: Chapter 1 Physical method Lagrangia
Page 18 and 19: Chapter 1 Physical method where F (
Page 20 and 21: Chapter 1 Physical method F (ν) (n
Page 22 and 23: Chapter 2 Lagrangian Description of
Page 34 and 35: Chapter 3 Compton Scattering and Su
Page 50 and 51: Chapter 4 Testing the Sum Rules in
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Chapter 4 Testing the Sum Rules in
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Chapter 5 Quantum One-Loop Correcti
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Chapter 6 Conclusion and Outlook We
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Appendix A Feynman Rules A.1 Feynma
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A.2 Plane Wave Expansions A.2 Plane
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A.2 Plane Wave Expansions Contracti
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Appendix B Loop Integration Im l 0
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Appendix B Loop Integration It is u
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Appendix C Diagrams µ q β p k k
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Bibliography [A + 06] J. Alcaraz et
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Bibliography [DHK + 04] [DKT01] [DP
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Bibliography [Nus72] [Pai67] [Pai68
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Acknowledgements First and foremost
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