Yorikiyo Nagashima

Elementary Particle Physics
Volume 1: Quantum Field Theory and Particles

WILEY-VCH Verlag GmbH & Co. KGaA


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Yorikiyo Nagashima
Elementary Particle Physics

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Yorikiyo Nagashima


Elementary Particle Physics
Volume 1: Quantum Field Theory and Particles

WILEY-VCH Verlag GmbH & Co. KGaA

www.pdfgrip.com


The Author
Yorikiyo Nagashima
Osaka University
Japan

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

All books published by Wiley-VCH are carefully
produced. Nevertheless, authors, editors, and
publisher do not warrant the information
contained in these books, including this book, to
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mind that statements, data, illustrations,
procedural details or other items may
inadvertently be inaccurate.
Library of Congress Card No.: applied for
British Library Cataloguing-in-Publication Data:
A catalogue record for this book is available

from the British Library.
Bibliographic information published by the
Deutsche Nationalbibliothek
The Deutsche Nationalbibliothek lists this
publication in the Deutsche Nationalbibliografie;
detailed bibliographic data are available on the
Internet at .
© 2010 WILEY-VCH Verlag GmbH & Co. KGaA,
Weinheim
All rights reserved (including those of translation
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Cover Design Adam Design, Weinheim
Printed in the Federal Republic of Germany
Printed on acid-free paper
ISBN 978-3-527-40962-4

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V


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

Elementary Particle Physics, Volume 1: Quantum Field Theory and Particles. Yorikiyo Nagashima
Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

ISBN: 978-3-527-40962-4

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VII

Contents
Foreword V
Preface XVII
Acknowledgements XXI
Part One A Field Theoretical Approach 1
1
1.1
1.1.1
1.1.2
1.1.3
1.2

Introduction 3
An Overview of the Standard Model 3
What is an Elementary Particle? 3
The Four Fundamental Forces and Their Unification 4
The Standard Model 7
The Accelerator as a Microscope 11

2

2.1
2.2
2.2.1
2.2.2
2.2.3
2.2.4
2.2.5
2.3
2.4

Particles and Fields 13
What is a Particle? 13
What is a Field? 21
Force Field 21
Relativistic Wave Equation 25
Matter Field 27
Intuitive Picture of a Field and Its Quantum 28
Mechanical Model of a Classical Field 29
Summary 32
Natural Units 33

3
3.1
3.2
3.2.1
3.2.2
3.3
3.4
3.4.1
3.4.2

3.4.3

Lorentz Invariance 37
Rotation Group 37
Lorentz Transformation 41
General Formalism 41
Lorentz Vectors and Scalars 43
Space Inversion and Time Reversal 45
Covariant Formalism 47
Tensors 47
Covariance 48
Supplementing the Time Component 49

Elementary Particle Physics, Volume 1: Quantum Field Theory and Particles. Yorikiyo Nagashima
Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
ISBN: 978-3-527-40962-4

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VIII

Contents

3.4.4
3.5
3.6

Rapidity 51
Lorentz Operator 53

Poincaré Group* 56

4
4.1
4.1.1
4.1.2
4.1.3
4.1.4
4.2
4.3
4.3.1
4.3.2
4.3.3
4.3.4
4.3.5
4.4

Dirac Equation 59
Relativistic Schrödinger Equation 59
Dirac Matrix 59
Weyl Spinor 61
Interpretation of the Negative Energy 64
Lorentz-Covariant Dirac Equation 69
Plane-Wave Solution 71
Properties of the Dirac Particle 75
Magnetic Moment of the Electron 75
Parity 77
Bilinear Form of the Dirac Spinor 78
Charge Conjugation 79
Chiral Eigenstates 82

Majorana Particle 84

5
5.1
5.1.1
5.1.2
5.1.3
5.1.4
5.2
5.2.1
5.2.2
5.3
5.3.1
5.3.2
5.3.3
5.3.4
5.4
5.5
5.5.1

Field Quantization 89
Action Principle 89
Equations of Motion 89
Hamiltonian Formalism 90
Equation of a Field 91
Noether’s Theorem 95
Quantization Scheme 100
Heisenberg Equation of Motion 100
Quantization of the Harmonic Oscillator 102
Quantization of Fields 105

Complex Fields 106
Real Field 111
Dirac Field 112
Electromagnetic Field 114
Spin and Statistics 119
Vacuum Fluctuation 121
The Casimir Effect* 122

6
6.1
6.2
6.3
6.3.1
6.4
6.4.1
6.4.2
6.5

Scattering Matrix 127
Interaction Picture 127
Asymptotic Field Condition 131
Explicit Form of the S-Matrix 133
Rutherford Scattering 135
Relativistic Kinematics 136
Center of Mass Frame and Laboratory Frame 136
Crossing Symmetry 139
Relativistic Cross Section 141

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Contents

6.5.1
6.5.2
6.5.3
6.5.4
6.5.5
6.6
6.6.1
6.6.2
6.7
6.7.1
6.7.2
6.7.3
6.7.4
6.8

Transition Rate 141
Relativistic Normalization 142
Incoming Flux and Final State Density 144
Lorentz-Invariant Phase Space 145
Cross Section in the Center of Mass Frame 145
Vertex Functions and the Feynman Propagator 147
e e γ Vertex Function 147
Feynman Propagator 151
Mott Scattering 157
Cross Section 157
Coulomb Scattering and Magnetic Scattering 161
Helicity Conservation 161

A Method to Rotate Spin 161
Yukawa Interaction 162

7
7.1
7.1.1
7.1.2
7.1.3
7.2
7.3
7.3.1
7.4

Qed: Quantum Electrodynamics 167
e–μ Scattering 167
Cross Section 167
Elastic Scattering of Polarized e–μ 171
e e C ! μ μ C Reaction 174
Compton Scattering 176
Bremsstrahlung 181
Soft Bremsstrahlung 183
Feynman Rules 186

8
8.1
8.1.1
8.1.2
8.1.3
8.1.4
8.1.5

8.1.6
8.1.7
8.1.8
8.2
8.2.1
8.2.2
8.2.3
8.2.4

Radiative Corrections and Tests of Qed* 191
Radiative Corrections and Renormalization* 191
Vertex Correction 191
Ultraviolet Divergence 193
Infrared Divergence 197
Infrared Compensation to All Orders* 199
Running Coupling Constant 204
Mass Renormalization 208
Ward–Takahashi Identity 210
Renormalization of the Scattering Amplitude 211
Tests of QED 213
Lamb Shift 213
g 2 214
Limit of QED Applicability 216
E821 BNL Experiment 216

9
9.1
9.1.1
9.1.2
9.2


Symmetries 221
Continuous Symmetries 222
Space and Time Translation 223
Rotational Invariance in the Two-Body System
Discrete Symmetries 233

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227

IX


X

Contents

9.2.1
9.2.2
9.3
9.3.1
9.3.2
9.3.3
9.3.4

Parity Transformation 233
Time Reversal 240
Internal Symmetries 251
U(1) Gauge Symmetry 251

Charge Conjugation 252
CPT Theorem 258
SU(2) (Isospin) Symmetry 260

10
10.1
10.1.1
10.1.2
10.2
10.2.1
10.2.2
10.3
10.3.1
10.3.2
10.3.3
10.4
10.4.1
10.4.2
10.5
10.5.1
10.5.2
10.6
10.6.1
10.6.2
10.6.3
10.7

Path Integral: Basics 267
Introduction 267
Bra and Ket 267

Translational Operator 268
Quantum Mechanical Equations 271
Schrödinger Equation 271
Propagators 272
Feynman’s Path Integral 274
Sum over History 274
Equivalence with the Schrödinger Equation 278
Functional Calculus 279
Propagators: Simple Examples 282
Free-Particle Propagator 282
Harmonic Oscillator 285
Scattering Matrix 294
Perturbation Expansion 295
S-Matrix in the Path Integral 297
Generating Functional 300
Correlation Functions 300
Note on Imaginary Time 302
Correlation Functions as Functional Derivatives 304
Connection with Statistical Mechanics 306

11
11.1
11.2
11.2.1
11.2.2
11.2.3
11.2.4
11.2.5
11.3
11.3.1

11.3.2
11.4
11.4.1
11.4.2
11.4.3

Path Integral Approach to Field Theory 311
From Particles to Fields 311
Real Scalar Field 312
Generating Functional 312
Calculation of det A 315
n-Point Functions and the Feynman Propagator 318
Wick’s Theorem 319
Generating Functional of Interacting Fields 320
Electromagnetic Field 321
Gauge Fixing and the Photon Propagator 321
Generating Functional of the Electromagnetic Field 323
Dirac Field 324
Grassmann Variables 324
Dirac Propagator 331
Generating Functional of the Dirac Field 332

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Contents

11.5
11.5.1
11.5.2

11.5.3
11.6
11.6.1
11.6.2
11.6.3
11.6.4
11.6.5
11.6.6
11.6.7
11.7
11.7.1
11.7.2
11.7.3

Reduction Formula 333
Scalar Fields 333
Electromagnetic Field 337
Dirac Field 337
QED 340
Formalism 340
Perturbative Expansion 342
First-Order Interaction 343
Mott Scattering 345
Second-Order Interaction 346
Scattering Matrix 351
Connected Diagrams 353
Faddeev–Popov’s Ansatz* 354
A Simple Example* 355
Gauge Fixing Revisited* 356
Faddeev–Popov Ghost* 359


12
12.1
12.2
12.2.1
12.2.2
12.2.3
12.3
12.3.1
12.3.2
12.3.3
12.4
12.4.1
12.4.2
12.4.3
12.4.4
12.4.5
12.4.6
12.5
12.5.1
12.5.2
12.5.3
12.5.4
12.6
12.7
12.7.1
12.7.2
12.7.3

Accelerator and Detector Technology 363

Accelerators 363
Basic Parameters of Accelerators 364
Particle Species 364
Energy 366
Luminosity 367
Various Types of Accelerators 369
Low-Energy Accelerators 369
Synchrotron 373
Linear Collider 377
Particle Interactions with Matter 378
Some Basic Concepts 378
Ionization Loss 381
Multiple Scattering 389
Cherenkov and Transition Radiation 390
Interactions of Electrons and Photons with Matter
Hadronic Shower 401
Particle Detectors 403
Overview of Radioisotope Detectors 403
Detectors that Use Light 404
Detectors that Use Electric Signals 410
Functional Usage of Detectors 415
Collider Detectors 422
Statistics and Errors 428
Basics of Statistics 428
Maximum Likelihood and Goodness of Fit 433
Least Squares Method 438

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XI


XII

Contents

Part Two

A Way to the Standard Model

441

13
13.1
13.2
13.3
13.3.1
13.3.2
13.3.3
13.3.4
13.4
13.5
13.5.1
13.5.2
13.5.3
13.5.4
13.6
13.6.1

13.6.2
13.7
13.7.1
13.7.2

Spectroscopy 443
Pre-accelerator Age (1897–1947) 444
Pions 449
π N Interaction 454
Isospin Conservation 454
Partial Wave Analysis 462
Resonance Extraction 466
Argand Diagram: Digging Resonances
(770) 475
Final State Interaction 478
Dalitz Plot 478
K Meson 481
Angular Momentum Barrier 484
ω Meson 485
Low-Energy Nuclear Force 487
Spin–Isospin Exchange Force 487
Effective Range 490
High-Energy Scattering 491
Black Sphere Model 491
Regge Trajectory* 494

14
14.1
14.1.1
14.1.2

14.1.3
14.1.4
14.1.5
14.1.6
14.2
14.2.1
14.2.2
14.2.3
14.3
14.4
14.4.1
14.4.2
14.5
14.5.1
14.5.2
14.5.3
14.5.4
14.5.5
14.5.6

The Quark Model 501
S U(3) Symmetry 501
The Discovery of Strange Particles 502
The Sakata Model 505
Meson Nonets 507
The Quark Model 509
Baryon Multiplets 510
General Rules for Composing Multiplets 511
Predictions of SU(3) 513
Gell-Mann–Okubo Mass Formula 513

Prediction of Ω 514
Meson Mixing 516
Color Degrees of Freedom 519
S U(6) Symmetry 522
Spin and Flavor Combined 522
S U(6) O(3) 525
Charm Quark 525
J/ψ 525
Mass and Quantum Number of J/ψ 527
Charmonium 527
Width of J/ψ 533
Lifetime of Charmed Particles 536
Charm Spectroscopy: SU(4) 537

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Contents

14.5.7
14.6
14.6.1
14.6.2
14.6.3
14.6.4

The Fifth Quark b (Bottom) 539
Color Charge 539

Color Independence 542
Color Exchange Force 544
Spin Exchange Force 545
Mass Formulae of Hadrons 547

15
15.1
15.2
15.2.1
15.2.2
15.2.3
15.3
15.3.1
15.3.2
15.4
15.4.1
15.4.2
15.4.3
15.4.4
15.5
15.5.1
15.5.2
15.6
15.6.1
15.6.2
15.6.3
15.6.4
15.7
15.7.1
15.7.2

15.7.3
15.7.4
15.8
15.8.1
15.8.2
15.8.3

Weak Interaction 553
Ingredients of the Weak Force 553
Fermi Theory 555
Beta Decay 555
Parity Violation 562
π Meson Decay 564
Chirality of the Leptons 567
Helicity and Angular Correlation 567
Electron Helicity 569
The Neutrino 571
Detection of the Neutrino 571
Mass of the Neutrino 572
Helicity of the Electron Neutrino 576
The Second Neutrino ν μ 578
The Universal V–A Interaction 579
Muon Decay 579
CVC Hypothesis 584
Strange Particle Decays 589
ΔS D ΔQ Rule 589
Δ I D 1/2 Rule 591
K l3 W K C ! π 0 C l C C ν 592
Cabibbo Rotation 596
Flavor Conservation 598

GIM Mechanism 598
Kobayashi–Maskawa Matrix 600
Tau Lepton 601
The Generation Puzzle 605
A Step Toward a Unified Theory 608
Organizing the Weak Phenomena 608
Limitations of the Fermi Theory 610
Introduction of SU(2) 614

16
16.1
16.1.1
16.1.2
16.1.3
16.1.4

Neutral Kaons and CP Violation* 617
Introduction 618
Strangeness Eigenstates and CP Eigenstates 618
0
Schrödinger Equation for K 0 K States 619
Strangeness Oscillation 622
Regeneration of K1 626

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XIV


Contents

16.1.5
16.2
16.2.1
16.2.2
16.3
16.3.1
16.3.2
16.4
16.4.1
16.4.2
16.4.3
16.4.4
16.5
16.5.1
16.5.2
16.6

Discovery of CP Violation 630
Formalism of CP and CPT Violation 632
CP, T, CPT Transformation Properties 632
Definition of CP Parameters 635
CP Violation Parameters 640
Observed Parameters 640
and 0 644
Test of T and CPT Invariance 653
Definition of T- and CPT-Violating Amplitudes 654
T Violation 654

CPT violation 656
Possible Violation of Quantum Mechanics 662
Experiments on CP Parameters 664
CPLEAR 664
NA48/KTeV 666
Models of CP Violation 673

17
17.1
17.2
17.3
17.4
17.4.1
17.4.2
17.5
17.5.1
17.5.2
17.6
17.6.1
17.6.2
17.6.3
17.7
17.7.1
17.7.2
17.8
17.8.1
17.8.2
17.8.3
17.8.4
17.8.5

17.9
17.9.1
17.9.2
17.10

Hadron Structure 679
Historical Overview 679
Form Factor 680
e–p Elastic Scattering 683
Electron Proton Deep Inelastic Scattering 687
Cross-Section Formula for Inelastic Scattering 687
Bjorken Scaling 690
Parton Model 693
Impulse Approximation 693
Electron–Parton Scattering 696
Scattering with Equivalent Photons 699
Transverse and Longitudinal Photons 699
Spin of the Target 702
Photon Flux 703
How to Do Neutrino Experiments 705
Neutrino Beams 705
Neutrino Detectors 709
ν–p Deep Inelastic Scattering 712
Cross Sections and Structure Functions 712
ν, ν–q Scattering 715
Valence Quarks and Sea Quarks 716
Comparisons with Experimental Data 717
Sum Rules 719
Parton Model in Hadron–Hadron Collisions 721
Drell–Yan Process 721

Other Hadronic Processes 724
A Glimpse of QCD’s Power 725

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Contents

18
18.1
18.2
18.2.1
18.2.2
18.2.3
18.2.4
18.2.5
18.2.6
18.2.7
18.2.8
18.3
18.4
18.4.1
18.4.2
18.4.3
18.5
18.5.1
18.5.2
18.6
18.6.1
18.6.2

18.6.3
18.6.4
18.6.5

Gauge Theories 729
Historical Prelude 729
Gauge Principle 731
Formal Definition 731
Gravity as a Geometry 733
Parallel Transport and Connection 734
Rotation in Internal Space 737
Curvature of a Space 739
Covariant Derivative 741
Principle of Equivalence 743
General Relativity and Gauge Theory 745
Aharonov–Bohm Effect 748
Nonabelian Gauge Theories 754
Isospin Operator 754
Gauge Potential 755
Isospin Force Field and Equation of Motion 757
QCD 760
Asymptotic Freedom 762
Confinement 767
Unified Theory of the Electroweak Interaction 770
S U(2) U(1) Gauge Theory 770
Spontaneous Symmetry Breaking 774
Higgs Mechanism 778
Glashow–Weinberg–Salam Electroweak Theory 782
Summary of GWS Theory 784


19
19.1
19.2
19.2.1
19.2.2
19.2.3
19.2.4
19.2.5
19.2.6
19.2.7

Epilogue 787
Completing the Picture 788
Beyond the Standard Model 789
Neutrino Oscillation 789
GUTs: Grand Unified Theories 791
Supersymmetry 792
Superstring Model 795
Extra Dimensions 796
Dark Matter 797
Dark Energy 798

Appendix A Spinor Representation 803
A.1
Definition of a Group 803
A.1.1 Lie Group 804
A.2
S U(2) 805
A.3
Lorentz Operator for Spin 1/2 Particle 809

A.3.1 S L(2, C ) Group 809
A.3.2 Dirac Equation: Another Derivation 811

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Contents

Appendix B Coulomb Gauge 813
B.1
Quantization of the Electromagnetic Field in the Coulomb Gauge 814
Appendix C Dirac Matrix and Gamma Matrix Traces 817
C.1
Dirac Plane Wave Solutions 817
C.2
Dirac γ Matrices 817
C.2.1 Traces of the γ Matrices 818
C.2.2 Levi-Civita Antisymmetric Tensor 819
C.3
Spin Sum of jM f i j2 819
C.3.1 A Frequently Used Example 820
C.3.2 Polarization Sum of the Vector Particle 822
C.4
Other Useful Formulae 823
Appendix D Dimensional Regularization 825
D.1

Photon Self-Energy 825
D.2
Electron Self-Energy 830
Appendix E Rotation Matrix 833
E.1
Angular Momentum Operators 833
E.2
Addition of the Angular Momentum 835
E.3
Rotational Matrix 835
Appendix F C, P, T Transformation 839
Appendix G S U(3), S U(n) and the Quark Model 841
G.1
Generators of the Group 841
G.1.1 Adjoint Representation 842
G.1.2 Direct Product 843
G.2
SU(3) 844
G.2.1 Structure Constants 844
G.2.2 Irreducible Representation of a Direct Product 846
G.2.3 Tensor Analysis 851
G.2.4 Young Diagram 854
Appendix H Mass Matrix and Decaying States 859
H.1
The Decay Formalism 859
Appendix I Answers to the Problems 865
Appendix J Particle Data 915
Appendix K Constants 917
References 919
Index 929


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XVII

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
Elementary Particle Physics, Volume 1: Quantum Field Theory and Particles. Yorikiyo Nagashima
Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
ISBN: 978-3-527-40962-4

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XVIII

Preface

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-bystep 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.

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Preface


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 selfcontained 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.

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XIX


XX

Preface

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

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XXI

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;
Elementary Particle Physics, Volume 1: Quantum Field Theory and Particles. Yorikiyo Nagashima
Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
ISBN: 978-3-527-40962-4

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XXII

Acknowledgements

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.

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Part One

A Field Theoretical Approach

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