Effective Lagrangians for the Standard Model

ISBN-13: 9783642638893 / Angielski / Miękka / 2013 / 316 str.

Antonio Dobado; Angel Gomez-Nicola; Antonio L. Maroto

Opis

This book is devoted to some recently developed techniques in quantum field theory (QFT), as well as to their main applications to different areas of parti cle physics. All together they are known as the effective or phenomenological Lagrangian formalism. Motivated by the enormous amount of work carried out in this field during the last years, our purpose when writing this book has been to give a modern and pedagogical exposition of the most relevant as pects of the topic. We hope that our efforts will be useful, both for graduated students in the search for a solid theoretical background in modern phe nomenology and for more experimented particle physicists willing to learn about this field or to start working on it. Even though we have tried to keep the book as self-contained as possible, it has been written assuming that the reader is familiar, at least, with the most basic concepts and techniques of QFT, gauge theories, the standard model (SM) and differential geometry, at the level of graduate studies. It is therefore possible that senior high-energy physicists may find the book too detailed and so they could probably omit several sections. The book is divided into two main parts and the appendices. In the first part we introduce the fundamentals of the effective Lagrangian formalism and other basic topics such as Ward identities, non-linear sigma models (NLSM), spontaneous symmetry breaking (SSB), anomalies, the SM symmetries, etc."

Spis treści

1. The Notion of Effective Lagrangian.- 1.1 Introduction.- 1.2 Integration of the Heavy Modes.- 1.2.1 The Effective Action for the Light Modes.- 1.2.2 Low Energy Expansions.- 1.3 The Decoupling Theorem.- 1.4 The Euler-Heisenberg Lagrangian.- 1.5 Theories with Spontaneous Symmetry Breaking.- 1.6 Decoupling of Chiral Fermions.- 1.7 References.- 2. Global Symmetries in Quantum Field Theory.- 2.1 Classical Symmetries.- 2.2 Green Functions and the Reduction Formula.- 2.3 Quantum Symmetries and Ward Identities.- 2.4 Spontaneous Symmetry Breaking and the Goldstone Theorem.- 2.5 Explicit Symmetry Breaking and the Dashen Conditions.- 2.6 References.- 3. The Non-linear ? Model.- 3.1 Introduction.- 3.2 The Geometry and the Dynamics of the Non-linear ? Model.- 3.3 The Quantum Non-linear ? Model.- 3.4 Reparametrization Invariance of the S-Matrix Elements.- 3.5 Local Symmetries and the Higgs Mechanism.- 3.6 Topologically Non-trivial Configurations.- 3.7 References.- 4. Anomalies.- 4.1 Introduction.- 4.2 The Axial Anomaly, Triangle Diagrams and the ?0 Decay.- 4.3 The Axial Anomaly and the Index Theorem.- 4.4 Gauge Anomalies.- 4.4.1 The Wess-Zumino Consistency Conditions.- 4.5 Regularization Methods.- 4.6 Ambiguities and Counterterms.- 4.7 Topological Interpretation of Non-Abelian Anomalies.- 4.8 Non-perturbative Anomalies.- 4.9 Non-linear ? Model Anomalies.- 4.10 The Wess-Zumino-Witten Term.- 4.10.1 Anomalous Processes in QCD.- 4.10.2 The Non-local Anomalous Effective Action.- 4.10.3 The WZW Term with Gauge Fields.- 4.10.4 Anomalous Processes and the WZW Term.- 4.10.5 The SU(2) WZW Term.- 4.11 The Trace Anomaly.- 4.12 References.- 5. The Symmetries of the Standard Model.- 5.1 The Elements of the Standard Model.- 5.1.1 Matter.- 5.1.2 Gauge Fields.- 5.1.3 The Symmetry Breaking Sector.- 5.2 The Cabibbo-Kobayashi-Maskawa Matrix and Weak CP Violation.- 5.3 The Cancellation of Gauge Anomalies in the Standard Model.- 5.4 Baryon and Lepton Number Anomalies in the Standard Model.- 5.5 The Evolution of the Coupling Constants.- 5.6 The Strong CP Problem.- 5.6.1 The ?-Vacuum.- 5.6.2 The Role of Instantons.- 5.6.3 The Strong CP Problem.- 5.7 The Symmetries of the Standard Model.- 5.8 References.- 6. The Effective Lagrangian for QCD.- 6.1 The QCD Lagrangian.- 6.2 QCD at Low Energies.- 6.3 The Chiral Lagrangian at Leading Order.- 6.4 The Chiral Lagrangian to Next to Leading Order.- 6.4.1 The L(4) Lagrangian.- 6.4.2 One-Loop Renormalization.- 6.4.3 The Effective Action to One Loop.- 6.5 The Low-Energy Constants.- 6.5.1 Phenomenological Estimates.- 6.5.2 Theoretical Estimates.- 6.5.3 The Nf = 2 Case.- 6.6 The Problem of Unitarity in ChPT.- 6.6.1 Unitarity and Dispersion Relations.- 6.6.2 The Large-N Limit.- 6.7 References.- 7. The Standard Model Symmetry Breaking Sector.- 7.1 The Mass Problem.- 7.2 The Effective Lagrangian for the SM Symmetry Breaking Sector.- 7.3 The O(p4) Lagrangian and One-Loop Renormalization.- 7.3.1 The 0(p4) Lagrangian.- 7.3.2 The Covariant Formalism.- 7.3.3 One-Loop Renormalization.- 7.4 The Heavy Higgs and QCD-Like Models.- 7.4.1 The Heavy Higgs Model.- 7.4.2 QCD-Like Models.- 7.5 Phenomenological Determination of the Chiral Parameters.- 7.5.1 Precision Tests of the Standard Model (Oblique Corrections).- 7.5.2 The Trilinear Gauge Boson Vertex.- 7.5.3 Elastic Gauge Boson Scattering.- 7.6 The Equivalence Theorem.- 7.6.1 Introduction.- 7.6.2 The Slavnov-Taylor Identities.- 7.6.3 The Reduction Formula.- 7.6.4 The Generalized Equivalence Theorem.- 7.6.5 The Equivalence Theorem.- 7.7 The Applicability of the Equivalence Theorem.- 7.8 Gauge Boson Scattering at High Energies.- 7.8.1 Dispersion Relations for the SM Symmetry Breaking Sector.- 7.8.2 The Large-N Limit: The Higgs and the General Case.- 7.9 References.- 8. Gravity and the Standard Model.- 8.1 Introduction.- 8.2 The Standard Model in Curved Space-Time.- 8.3 Anomalies in the Standard Model.- 8.3.1 The Leptonic and Baryonic Anomalies.- 8.3.2 Gauge Anomalies.- 8.3.3 Gravitational Anomalies.- 8.3.4 Charge Quantization in the SM.- 8.4 The Effect of Matter Fields on Gravitation.- 8.5 The Effective Action for Gravity.- 8.5.1 The Background Field Method in Quantum Gravity.- 8.5.2 General Effective Formalism.- 8.5.3 Quantum Corrections to the Newton Potential.- 8.5.4 Perspectives and Other Approaches.- 8.6 References.- A. Useful Formulae and Notation.- A.1 Notation in Minkowski Space-Time.- A.2 Notation in Euclidean Space-Time.- A.3 Useful Formulae.- B. Notes on Differential Geometry.- B.1 Riemannian Geometry.- B.2 Homogeneous Spaces.- B.3 The Geometry of Gauge Fields.- B.4 References.- C. Aspects of Quantum Field Theory.- C.1 Renormalization Group Equations.- C.2 Quantization of Gauge Theories and BRS Invariance.- C.3 The Background Field Method.- C.4 The Heat-Kernel Method.- C.5 References.- D. Unitarity and Partial Waves.- D.1 Unitarity.- D.2 Dispersion Relations.- D.3 NGB Amplitudes to O(p4).- D.4 References.

Blurb

This book presents a detailed and pedagogical exposition of the effective Lagrangian techniques and their applications to high-energy physics. It covers the main theoretical ideas and describes comprehensively how to use them in different fields, such as chiral perturbation theory and the symmetry breaking sector of the standard model and even low-energy quantum gravity. The book is written in the language of modern quantum field theory. Some of the theoretical topics treated are: decoupling, the Goldstone theorem, the non-linear sigma model, anomalies, the Wess--Zumino--Witten term, and the equivalence theorem.