Elementary Particle Physics E-Book

Yorikiyo Nagashima

• Herausgeber: Wiley-VCH
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 1255

Veröffentlichungsjahr: 2011

Beschreibung

ACCOUNTING PRINCIPLES

Meeting the need for a coherently written and comprehensive compendium combining field theory and particle physics for advanced students and researchers, this volume directly links the theory to the experiments. It is clearly divided into two sections covering approaches to field theory and the Standard Model, and rounded off with numerous useful appendices. A timely work for high energy and theoretical physicists, as well as astronomers, graduate students and lecturers in physics.

From the contents:

• Particles and Fields
• Lorentz Invariance
• Dirac Equation
• Field Quantization
• Scattering Matrix
• QED: Quantum Electrodynamics
• Radiative Corrections and Tests of Qed
• Symmetries
• Path Integral : Basics
• Path Integral Approach to Field Theory
• Accelerator and Detector Technology
• Spectroscopy
• The Quark Model
• Weak Interaction
• Neutral Kaons and CP Violation
• Hadron Structure
• Gauge Theories
• Appendices

Volume 2 (2013, ISBN 3-527-40966-1) will concentrate on the main aspects of the Standard Model by addressing its recent developments and future prospects. Furthermore, it will give some thought to intriguing ideas beyond the Standard Model, including the Higgs boson, the neutrino, the concepts of the Grand Unified Theory and supersymmetry, axions, and cosmological developments.

Leseprobe

Contents

Foreword

Preface

Acknowledgements

Part One A Field Theoretical Approach

1 Introduction

1.1 An Overview of the Standard Model

1.2 The Accelerator as a Microscope

2 Particles and Fields

2.1 What is a Particle?

2.2 What is a Field?

2.3 Summary

2.4 Natural Units

3 Lorentz Invariance

3.1 Rotation Group

3.2 Lorentz Transformation

3.3 Space Inversion and Time Reversal

3.4 Covariant Formalism

3.5 Lorentz Operator

3.6 Poincaré Group*

4 Dirac Equation

4.1 Relativistic Schrödinger Equation

4.2 Plane-Wave Solution

4.3 Properties of the Dirac Particle

4.4 Majorana Particle

5 Field Quantization

5.1 Action Principle

5.2 Quantization Scheme

5.3 Quantization of Fields

5.4 Spin and Statistics

5.5 Vacuum Fluctuation

6 Scattering Matrix

6.1 Interaction Picture

6.2 Asymptotic Field Condition

6.3 Explicit Form of the S-Matrix

6.4 Relativistic Kinematics

6.5 Relativistic Cross Section

6.6 Vertex Functions and the Feynman Propagator

6.7 Mott Scattering

6.8 Yukawa Interaction

7 Qed: Quantum Electrodynamics

7.1 e–μ Scattering

7.2 Compton Scattering

7.3 Bremsstrahlung

7.4 Feynman Rules

8 Radiative Corrections and Tests of Qed*

8.1 Radiative Corrections and Renormalization*

8.2 Tests of QED

9 Symmetries

9.1 Continuous Symmetries

9.2 Discrete Symmetries

9.3 Internal Symmetries

10 Path Integral: Basics

10.1 Introduction

10.2 Quantum Mechanical Equations

10.3 Feynman’s Path Integral

10.4 Propagators: Simple Examples

10.5 Scattering Matrix

10.6 Generating Functional

10.7 Connection with Statistical Mechanics

11 Path Integral Approach to Field Theory

11.1 From Particles to Fields

11.2 Real Scalar Field

11.3 Electromagnetic Field

11.4 Dirac Field

11.5 Reduction Formula

11.6 QED

11.7 Faddeev–Popov’s Ansatz*

12 Accelerator and Detector Technology

12.1 Accelerators

12.2 Basic Parameters of Accelerators

12.3 Various Types of Accelerators

12.4 Particle Interactions with Matter

12.5 Particle Detectors

12.6 Collider Detectors

12.7 Statistics and Errors

Part Two A Way to the Standard Model

13 Spectroscopy

13.1 Pre-accelerator Age (1897–1947)

13.2 Pions

13.3 πN Interaction

13.4 ρ (770)

13.5 Final State Interaction

13.6 Low-Energy Nuclear Force

13.7 High-Energy Scattering

14 The Quark Model

14.1 SU(3) Symmetry

14.2 Predictions of SU(3)

14.3 Color Degrees of Freedom

14.4 SU(6) Symmetry

14.5 Charm Quark

14.6 Color Charge

15 Weak Interaction

15.1 Ingredients of the Weak Force

15.2 Fermi Theory

15.3 Chirality of the Leptons

15.4 The Neutrino

15.5 The Universal V–A Interaction

15.6 Strange Particle Decays

15.7 Flavor Conservation

15.8 A Step Toward a Unified Theory

16 Neutral Kaons and CP Violation*

16.1 Introduction

16.2 Formalism of CP and CPT Violation

16.3 CP Violation Parameters

16.4 Test of T and CPT Invariance

16.5 Experiments on CP Parameters

16.6 Models of CP Violation

17 Hadron Structure

17.1 Historical Overview

17.2 Form Factor

17.3 e–p Elastic Scattering

17.4 Electron Proton Deep Inelastic Scattering

17.5 Parton Model

17.6 Scattering with Equivalent Photons

17.7 How to Do Neutrino Experiments

17.8 ν–p Deep Inelastic Scattering

17.9 Parton Model in Hadron–Hadron Collisions

17.10 A Glimpse of QCD’s Power

18 Gauge Theories

18.1 Historical Prelude

18.2 Gauge Principle

18.3 Aharonov–Bohm Effect

18.4 Nonabelian Gauge Theories

18.5 QCD

18.6 Unified Theory of the Electroweak Interaction

19 Epilogue

19.1 Completing the Picture

19.2 Beyond the Standard Model

Appendix A Spinor Representation

A.1 Definition of a Group

A.2 SU(2)

A.3 Lorentz Operator for Spin 1/2 Particle

Appendix B Coulomb Gauge

B.1 Quantization of the Electromagnetic Field in the Coulomb Gauge

Appendix C Dirac Matrix and Gamma Matrix Traces

C.1 Dirac Plane Wave Solutions

C.2 Dirac γ Matrices

C.3 Spin Sum of |fi|2

C.4 Other Useful Formulae

Appendix D Dimensional Regularization

D.1 Photon Self-Energy

D.2 Electron Self-Energy

Appendix E Rotation Matrix

E.1 Angular Momentum Operators

E.2 Addition of the Angular Momentum

E.3 Rotational Matrix

Appendix F C, P, T Transformation

Appendix G SU(3), SU(n) and the Quark Model

G.1 Generators of the Group

G.2 SU(3)

Appendix H Mass Matrix and Decaying States

H.1 The Decay Formalism

Appendix I Answers to the Problems

Appendix J Particle Data

Appendix K Constants

References

Index

Related Titles

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The Author

Yorikiyo NagashimaOsaka [email protected]

Cover Image

Japanese symbol that denotes “void” or “nothing”; also symbolizes “supreme state of matter” or “spirit”.

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Foreword

This is a unique book. It covers the entire theoretical and experimental content of particle physics.

Particle physics sits at the forefront of our search for the ultimate structure of matter at the smallest scale, but in the process it has also learned to question the nature of our space and time in which they exist. Going hand in hand with technological advances, particle physics now has extended its reach to studies of the structure and the history of the universe. It seems that both the ultimate small and the ultimate large are linked together. To explore one you must also explore the other.

Thus particle physics covers a vast area. To master it, you usually have to read different books, at increasingly advanced levels, on individual subjects like its historical background, basic experimental data, quantum field theory, mathematical concepts, theoretical models, cosmological concepts, etc. This book covers most of those topics in a single volume in an integrated manner. Not only that, it shows you how to derive each important mathematical formula in minute detail, then asks you to work out many problems, with answers given at the end of the book. Some abstract formulas are immediately followed by their intuitive interpretation and experimental consequences. The same topics are often repeated at different levels of sophistication in different chapters as you read on, which will help deepen your understanding.

All these features are quite unique to this book, and will be most helpful to students as well as laymen or non-experts who want to learn the subject seriously and enjoy it. It can serve both as a text book and as a compendium on particle physics. Even for practicing particle physicists and professors this will be a valuable reference book to keep at hand. Few people like Professor Nagashima, an accomplished experimental physicist who is also conversant with sophisticated theoretical subjects, could have written it.

Chicago, October 2009 Yoichiro Nambu

Preface

The purpose of this book is to present introductory explanations to junior graduate students of major advances in particle physics made in the last century. It is also aimed at laypeople who have not received a standard education in physics but are willing to make an extra effort to follow mathematical logic. Therefore it is organized to be suitable for self-study and is as self-contained as possible. This is why it starts with an introduction to field theory while the main purpose is to talk about particle physics. Quantum field theory is an essential mathematical tool for understanding particle physics, which has fused quantum mechanics with special relativity. However, phenomena that need the theory of relativity are almost completely limited to particle physics, cosmology and parts of astrophysics, which are not topics of everyday life. Few students dare to take a course in special or general relativity. This fact, together with the mathematical complexity of field theory, makes particle physics hard to approach. If one tries to make a self-contained explanation of mathematical aspects of the field, hardly any space is left for the details of particle-physics phenomena. While good textbooks on field theories are abundant, very few talk about the rich phenomena in the world of elementary particle physics. One reason may be that the experimental progress is so rapid that any textbook that tries to take an in-depth approach to the experimental aspect of the field becomes obsolete by the time it is published. In addition, when one makes a great effort to find a good book, basic formulae are usually given without explanation. The author had long felt the need for a good textbook suitable for a graduate course, well balanced between theory and experiment.

Without doubt many people have been fascinated by the world that quantum mechanics opens up. After a student has learned the secrets of its mystery, he (or she) must realize that his world view has changed for life. But at what depth would it have been if he thought he had grasped the idea without knowledge of the Schödinger equation? This is why the author feels uneasy with presentation of the basic formulae as given from heaven, as is often the case in many textbooks on experimental particle physics.

This book is the first of two volumes. Volume I paves the way to the Standard Model and Volume II develops applications and discusses recent progress.

Volume I, i.e. this book, is further divided into two parts, a field theoretical approach and the way to the Standard Model. The aim of Part I is to equip students with tools so they can calculate basic formulae to analyze the experimental data using quantized field theories at least at the tree level. Tailored to the above purpose, the author’s intention is to present a readable introduction and, hopefully, an intermediate step to the study of advanced field theories.

Chapters 1 and 2 are an introduction and outline of what the Standard Model is. Chapter 3 picks out essential ingredients of special relativity relevant for particle physics and prepares for easy understanding of relativistic formulae that follow. Chapters 4–7, starting from the Dirac equation, field quantization, the scattering matrix and leading to QED (quantum electrodynamics), should be treated as one, closed subject to provide basic knowledge of relativistic field theories and step-by-step acquisition of the necessary tools for calculating various dynamic processes. For the treatment of higher order radiative corrections, only a brief explanation is given in Chapter 8, to discuss how mathematical consistency of the whole theory is achieved by renormalization.

Chapter 9 deals with space-time and internal symmetry, somewhat independent topics that play a double role as an introduction to the subject and appendices to particle physics, which is discussed in Part II.

Two chapters, 10 and 11, on the path integral are included as an addition. The method is very powerful if one wants to go into the formal aspects of field theory, including non-Abelian gauge theories, in any detail. Besides it is the modern way of interpreting quantum mechanics that has many applications in various fields, and the author felt acquaintance with the path integral is indispensable. However, from a practical point of view of calculating the tree-level formulae, the traditional canonical quantization method is all one needs. With all the new concepts and mathematical preparation, the chapter stops at a point where it has rederived what had already been calculated before. So readers have the choice of skipping these chapters and coming back later when their interest has been aroused.

By jumping to Chapter 18 which describes axioms of the Standard Model, the field theoretical approach can be concluded in a self-contained way, at least formally. But it was placed at the end of Part II because the phenomenological approach also culminates in the formulation of the unified gauge theories. Although two alternative approaches are prepared to reach the goal, the purpose of the book is to present particle physics, and field theory is to be considered as a tool and treated as such.

As part of the minimum necessary knowledge, a chapter was added at the end of Part I on basic techniques of experimental measurements, the other necessary tool to understand particle physics phenomena. Readers who are perplexed with the combination may skip this chapter, but it is the author’s wish that even students who aim at a theoretical career should understand at least this level of experimental techniques. After all, the essence of natural science is to explain facts and theorists should understand what the data really mean. In addition, a few representative experiments are picked out and scattered throughout the book with appropriate descriptions. They were chosen for their importance in physics but also in order to demonstrate how modern experiments are carried out.

In Part II, various particle phenomena are presented, the SU(3) group is introduced, basic formulae are calculated and explanations are given. The reader should be able to understand the quark structure of matter and basic rules on which the modern unified theory is constructed. Those who do not care how the formulae are derived may skip most of Part I and start from Part II, treating Part I as an appendix, although that is not what the author intended. Part II ends when the primary equations of the Standard Model of particle physics have been derived.

With this goal in mind, after presenting an overview of hadron spectroscopy in Chapter 13 and the quark model in Chapter 14, we concentrate mainly on the electro-weak force phenomena in Chapter 15 to probe their dynamical structure and explain processes that lead to a unified view of electromagnetic and weak interactions. Chapter 17 is on the hadron structure, a dynamical aspect of the quark model that has led to QCD. Chapter 18 presents the principles of gauge theory; its structure and physical interpretation are given. Understanding the axioms of the Standard Model is the goal of the whole book.

Chapter 16 on CP violation in K mesons is an exception to the outline described above. It was included for two reasons. First, because it is an old topic, dating back to 1964, and second, because it is also a new topic, which in author’s personal perception may play a decisive role in the future course of particle physics. However, discussions from the viewpoint of unified theories is deferred until we discuss the role of B-physics in Volume II. Important though it is, its study is a side road from the main route of reaching the Standard Model, and this chapter should be considered as a topic independent of the rest; one can study it when one’s interest is aroused.

Although the experimental data are all up-to-date, new phenomena that the Standard Model predicted and were discovered after its establishment in the early 1970s are deferred to Volume II. The last chapter concludes what remains to be done on the Standard Model and introduces some intriguing ideas about the future of particle physics.

Volume II, which has yet to come, starts with the axioms of gauge field theories and presents major experimental facts that the Standard Model predicted and whose foundations were subsequently established. These include W, Z, QCD jet phenomena and CP violation in B physics in both electron and hadron colliders. The second half of Volume II deals issues beyond the Standard Model and recent developments of particle physics, the Higgs, the neutrino, grand unified theories, unsolved problems in the Standard Model, such as axions, and the connection with cosmology.

A knowledge of quantum mechanics and the basics of special relativity is required to read this book, but that is all that is required. One thing the author aimed at in writing this series is to make a reference book so that it can serve as a sort of encyclopedia later on. For that reason, each chapter is organized to be as self-contained as possible. The list of references is extensive on purpose. Also, as a result, some chapters include sections that are at higher level than that the reader has learned up to that point. An asterisk * is attached to those sections and problems. If the reader feels they are hard, there is no point in getting stuck there, skip it and come back later.

This book was based on a series of books originally written in Japanese and published by Asakura Shoten of Tokyo ten years ago. Since then, the author has reorganized and reformulated them with appropriate updating so that they can be published not as a translation but as new books.

Osaka, October, 2009 Yorikiyo Nagashima

Acknowledgements

The author wishes to thank Professor J. Arafune (Tokyo University) for valuable advice and Professors T. Kubota and T. Yamanaka (Osaka University) for reading part of the manuscript and for giving many useful suggestions. Needless to say, any mistakes are entirely the author’s responsibility and he appreciates it if the reader notifies them to him whenever possible.

The author would like to express his gratitude to the authors cited in the text and to the following publishers for permission to reproduce various photographs, figures and diagrams:

American Institute of Physics, publisher of Physics Today for permission to reproduce Figure 19.4;American Physical Society, publisher of the Physical Review, Physical Review Letters and the Review of Modern Physics, for permission to reproduce Figures 4.3, 5.2ab, 8.8, 9.2, 9.3ab, 12.18abc, 13.11a, 13.17, 13.19, 13.21, 13.23, 13.24ab, 14.6, 14.13–15, 14.20b, 14.25, 14.30, 15.3ab, 15.13, 15.15, 15.17a, 15.21, 16.5–7ab, 16.19, 16.21–23, 17.2b–17.7, 17.12c, 17.15a, 17.21ab, 18.10ab, 18.11abc;Annual Reviews, publisher of Annual Review of Nuclear and Particle Science for permission to reproduce Figures 12.23ab, 13.29, 14.18, 17.11;Elsevier Science Ltd., publisher of Nuclear Physics, Physics Letters, Physics Report, for permission to reproduce Figures 8.9ab, 12.24, 12.25, 12.29, 12.33ab, 12.35ab, 12.37, 12.40–42, 13.14abcd, 13.18, 13.30, 15.8, 15.17b, 15.22, 15.23, 16.1b, 16.8ab–16.10ab, 16.12, 16.13, 16.15–17ab, 17.19, 18.18;Institute of Physics Publishing Ltd., publisher of Report on Progress of Physics for permission to reproduce Figures 15.11 and 15.12;Japan Physical Society, publisher of Butsuri for permission to reproduce Figure 12.26b;Nature Publishing Group, publisher of Nature for permission to reproduce Figures 13.5 and 14.1;Particle Data Group, publisher of Review of Particle Physics for permission to reproduce Figures 12.10, 12.15–12.17, 12.20, 12.28b, 12.30ab, 12.38, 12.47, 13.25, 13.26, 14.11, 14.16, 14.24, 14.26, 17.17, 18.16;Royal Society, publisher of the Proceedings of the Royal Society for permission to reproduce Figure 13.4;Shokabo, publisher of the Cosmic Rays for permission to reproduce Figure 12.22;Springer Verlag, publisher of Zeitschrift für Physik and European Journal of Physics for permission to reproduce Figures 12.43, 16.18, 17.14c, 17.15b, 17.18ab, 17.24.

Part One A Field Theoretical Approach

2

Particles and Fields

In particle physics, a particle is defined as an energy quantum associated with a “field”. The field is an entity that is defined over all space and time (collectively called space-time) and is able to produce waves, according to classical physics, or quanta, in present day terminology, when excited or when some amount of energy is injected. In a microworld the quanta are observed as particles, but collectively they behave like waves. A quantum is the name given to an object that possesses the dual properties of both a particle and a wave. A typical example of a field is the electromagnetic field. It is created by a charge and extends all over space. It is static when the charge that creates it does not move, but it can be excited by vibrating the source of the field, the electric charge; then the vibrating field propagates. This is a charge radiating an electromagnetic wave. It is well known that historically quantum mechanics has its origin in Planck’s recognition that blackbody radiation is a collection of countable quanta, photons.

In 19th century physics, waves could only be transmitted by some kind of vibrating medium and the electromagnetic waves were considered to propagate in a medium called the “ether”. The existence of the ether was ruled out with the advent of special relativity, and people began to consider that the vacuum, though void of anything in the classical sense, has the built-in property of producing all kinds of fields, whose excitations are observed as quanta or particles. The Standard Model has advanced the idea that the vacuum is not an empty entity but rather filled with various kinds of exotic material, including the Higgs particle, and exhibits dynamical properties like those observed in ordinary matter. The vacuum as we view it nowadays is a kind of resurrected ether with strange attributes that nobody had thought of. In this chapter, we describe an intuitive picture of both particles and fields, define some associated variables and prepare basic tools and terminologies necessary for the treatment of quantum field theory.