Elementary Particle Physics: Quantum Field Theory and Particles V1

Elementary Particle Physics
Foreword
Contents
Preface
Acknowledgements
Part One A Field Theoretical Approach
1 Introduction
1.1 An Overview of the Standard Model
1.1.1 What is an Elementary Particle?
1.1.2 The Four Fundamental Forces and Their Unification
1.1.3 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?
2.2.1 Force Field
2.2.2 Relativistic Wave Equation
2.2.3 Matter Field
2.2.4 Intuitive Picture of a Field and Its Quantum
2.2.5 Mechanical Model of a Classical Field
2.3 Summary
2.4 Natural Units
3 Lorentz Invariance
3.1 Rotation Group
3.2 Lorentz Transformation
3.2.1 General Formalism
3.2.2 Lorentz Vectors and Scalars
3.3 Space Inversion and Time Reversal
3.4 Covariant Formalism
3.4.1 Tensors
3.4.2 Covariance
3.4.3 Supplementing the Time Component
3.4.4 Rapidity
3.5 Lorentz Operator
3.6 Poincaré Group*
4 Dirac Equation
4.1 Relativistic Schrödinger Equation
4.1.1 Dirac Matrix
4.1.2 Weyl Spinor
4.1.3 Interpretation of the Negative Energy
4.1.4 Lorentz-Covariant Dirac Equation
4.2 Plane-Wave Solution
4.3 Properties of the Dirac Particle
4.3.1 Magnetic Moment of the Electron
4.3.2 Parity
4.3.3 Bilinear Form of the Dirac Spinor
4.3.4 Charge Conjugation
4.3.5 Chiral Eigenstates
4.4 Majorana Particle
5 Field Quantization
5.1 Action Principle
5.1.1 Equations of Motion
5.1.2 Hamiltonian Formalism
5.1.3 Equation of a Field
5.1.4 Noether's Theorem
5.2 Quantization Scheme
5.2.1 Heisenberg Equation of Motion
5.2.2 Quantization of the Harmonic Oscillator
5.3 Quantization of Fields
5.3.1 Complex Fields
5.3.2 Real Field
5.3.3 Dirac Field
5.3.4 Electromagnetic Field
5.4 Spin and Statistics
5.5 Vacuum Fluctuation
5.5.1 The Casimir Effect*
6 Scattering Matrix
6.1 Interaction Picture
6.2 Asymptotic Field Condition
6.3 Explicit Form of the S-Matrix
6.3.1 Rutherford Scattering
6.4 Relativistic Kinematics
6.4.1 Center of Mass Frame and Laboratory Frame
6.4.2 Crossing Symmetry
6.5 Relativistic Cross Section
6.5.1 Transition Rate
6.5.2 Relativistic Normalization
6.5.3 Incoming Flux and Final State Density
6.5.4 Lorentz-Invariant Phase Space
6.5.5 Cross Section in the Center of Mass Frame
6.6 Vertex Functions and the Feynman Propagator
6.6.1 ee Vertex Function
6.6.2 Feynman Propagator
6.7 Mott Scattering
6.7.1 Cross Section
6.7.2 Coulomb Scattering and Magnetic Scattering
6.7.3 Helicity Conservation
6.7.4 A Method to Rotate Spin
6.8 Yukawa Interaction
7 Qed: Quantum Electrodynamics
7.1 e-- Scattering
7.1.1 Cross Section
7.1.2 Elastic Scattering of Polarized e--
7.1.3 e-e+-+ Reaction
7.2 Compton Scattering
7.3 Bremsstrahlung
7.3.1 Soft Bremsstrahlung
7.4 Feynman Rules
8 Radiative Corrections and Tests of Qed*
8.1 Radiative Corrections and Renormalization*
8.1.1 Vertex Correction
8.1.2 Ultraviolet Divergence
8.1.3 Infrared Divergence
8.1.4 Infrared Compensation to All Orders*
8.1.5 Running Coupling Constant
8.1.6 Mass Renormalization
8.1.7 Ward–Takahashi Identity
8.1.8 Renormalization of the Scattering Amplitude
8.2 Tests of QED
8.2.1 Lamb Shift
8.2.2 g-2
8.2.3 Limit of QED Applicability
8.2.4 E821 BNL Experiment
9 Symmetries
9.1 Continuous Symmetries
9.1.1 Space and Time Translation
9.1.2 Rotational Invariance in the Two-Body System
9.2 Discrete Symmetries
9.2.1 Parity Transformation
9.2.2 Time Reversal
9.3 Internal Symmetries
9.3.1 U(1) Gauge Symmetry
9.3.2 Charge Conjugation
9.3.3 CPT Theorem
9.3.4 SU(2) (Isospin) Symmetry
10 Path Integral: Basics
10.1 Introduction
10.1.1 Bra and Ket
10.1.2 Translational Operator
10.2 Quantum Mechanical Equations
10.2.1 Schrödinger Equation
10.2.2 Propagators
10.3 Feynman's Path Integral
10.3.1 Sum over History
10.3.2 Equivalence with the Schrödinger Equation
10.3.3 Functional Calculus
10.4 Propagators: Simple Examples
10.4.1 Free-Particle Propagator
10.4.2 Harmonic Oscillator
10.5 Scattering Matrix
10.5.1 Perturbation Expansion
10.5.2 S-Matrix in the Path Integral
10.6 Generating Functional
10.6.1 Correlation Functions
10.6.2 Note on Imaginary Time
10.6.3 Correlation Functions as Functional Derivatives
10.7 Connection with Statistical Mechanics
11 Path Integral Approach to Field Theory
11.1 From Particles to Fields
11.2 Real Scalar Field
11.2.1 Generating Functional
11.2.2 Calculation of detA
11.2.3 n-Point Functions and the Feynman Propagator
11.2.4 Wick's Theorem
11.2.5 Generating Functional of Interacting Fields
11.3 Electromagnetic Field
11.3.1 Gauge Fixing and the Photon Propagator
11.3.2 Generating Functional of the Electromagnetic Field
11.4 Dirac Field
11.4.1 Grassmann Variables
11.4.2 Dirac Propagator
11.4.3 Generating Functional of the Dirac Field
11.5 Reduction Formula
11.5.1 Scalar Fields
11.5.2 Electromagnetic Field
11.5.3 Dirac Field
11.6 QED
11.6.1 Formalism
11.6.2 Perturbative Expansion
11.6.3 First-Order Interaction
11.6.4 Mott Scattering
11.6.5 Second-Order Interaction
11.6.6 Scattering Matrix
11.6.7 Connected Diagrams
11.7 Faddeev–Popov's Ansatz*
11.7.1 A Simple Example*
11.7.2 Gauge Fixing Revisited*
11.7.3 Faddeev–Popov Ghost*
12 Accelerator and Detector Technology
12.1 Accelerators
12.2 Basic Parameters of Accelerators
12.2.1 Particle Species
12.2.2 Energy
12.2.3 Luminosity
12.3 Various Types of Accelerators
12.3.1 Low-Energy Accelerators
12.3.2 Synchrotron
12.3.3 Linear Collider
12.4 Particle Interactions with Matter
12.4.1 Some Basic Concepts
12.4.2 Ionization Loss
12.4.3 Multiple Scattering
12.4.4 Cherenkov and Transition Radiation
12.4.5 Interactions of Electrons and Photons with Matter
12.4.6 Hadronic Shower
12.5 Particle Detectors
12.5.1 Overview of Radioisotope Detectors
12.5.2 Detectors that Use Light
12.5.3 Detectors that Use Electric Signals
12.5.4 Functional Usage of Detectors
12.6 Collider Detectors
12.7 Statistics and Errors
12.7.1 Basics of Statistics
12.7.2 Maximum Likelihood and Goodness of Fit
12.7.3 Least Squares Method
Part Two A Way to the Standard Model
13 Spectroscopy
13.1 Pre-accelerator Age (1897–1947)
13.2 Pions
13.3 N Interaction
13.3.1 Isospin Conservation
13.3.2 Partial Wave Analysis
13.3.3 Resonance Extraction
13.3.4 Argand Diagram: Digging Resonances
13.4 (770)
13.5 Final State Interaction
13.5.1 Dalitz Plot
13.5.2 K Meson
13.5.3 Angular Momentum Barrier
13.5.4 Meson
13.6 Low-Energy Nuclear Force
13.6.1 Spin–Isospin Exchange Force
13.6.2 Effective Range
13.7 High-Energy Scattering
13.7.1 Black Sphere Model
13.7.2 Regge Trajectory*
14 The Quark Model
14.1 SU(3) Symmetry
14.1.1 The Discovery of Strange Particles
14.1.2 The Sakata Model
14.1.3 Meson Nonets
14.1.4 The Quark Model
14.1.5 Baryon Multiplets
14.1.6 General Rules for Composing Multiplets
14.2 Predictions of SU(3)
14.2.1 Gell-Mann–Okubo Mass Formula
14.2.2 Prediction of
14.2.3 Meson Mixing
14.3 Color Degrees of Freedom
14.4 SU(6) Symmetry
14.4.1 Spin and Flavor Combined
14.4.2 SU(6)O(3)
14.5 Charm Quark
14.5.1 J/
14.5.2 Mass and Quantum Number of J/
14.5.3 Charmonium
14.5.4 Width of J/
14.5.5 Lifetime of Charmed Particles
14.5.6 Charm Spectroscopy: SU(4)
14.5.7 The Fifth Quark b (Bottom)
14.6 Color Charge
14.6.1 Color Independence
14.6.2 Color Exchange Force
14.6.3 Spin Exchange Force
14.6.4 Mass Formulae of Hadrons
15 Weak Interaction
15.1 Ingredients of the Weak Force
15.2 Fermi Theory
15.2.1 Beta Decay
15.2.2 Parity Violation
15.2.3 Meson Decay
15.3 Chirality of the Leptons
15.3.1 Helicity and Angular Correlation
15.3.2 Electron Helicity
15.4 The Neutrino
15.4.1 Detection of the Neutrino
15.4.2 Mass of the Neutrino
15.4.3 Helicity of the Electron Neutrino
15.4.4 The Second Neutrino
15.5 The Universal V–A Interaction
15.5.1 Muon Decay
15.5.2 CVC Hypothesis
15.6 Strange Particle Decays
15.6.1 S=Q Rule
15.6.2 I=1/2 Rule
15.6.3 Kl3: K+0+l++
15.6.4 Cabibbo Rotation
15.7 Flavor Conservation
15.7.1 GIM Mechanism
15.7.2 Kobayashi–Maskawa Matrix
15.7.3 Tau Lepton
15.7.4 The Generation Puzzle
15.8 A Step Toward a Unified Theory
15.8.1 Organizing the Weak Phenomena
15.8.2 Limitations of the Fermi Theory
15.8.3 Introduction of SU(2)
16 Neutral Kaons and CP Violation*
16.1 Introduction
16.1.1 Strangeness Eigenstates and CP Eigenstates
16.1.2 Schrödinger Equation for K0-K0 States
16.1.3 Strangeness Oscillation
16.1.4 Regeneration of K1
16.1.5 Discovery of CP Violation
16.2 Formalism of CP and CPT Violation
16.2.1 CP, T, CPT Transformation Properties
16.2.2 Definition of CP Parameters
16.3 CP Violation Parameters
16.3.1 Observed Parameters
16.3.2 and
16.4 Test of T and CPT Invariance
16.4.1 Definition of T- and CPT-Violating Amplitudes
16.4.2 T Violation
16.4.3 CPT violation
16.4.4 Possible Violation of Quantum Mechanics
16.5 Experiments on CP Parameters
16.5.1 CPLEAR
16.5.2 NA48/KTeV
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
17.4.1 Cross-Section Formula for Inelastic Scattering
17.4.2 Bjorken Scaling
17.5 Parton Model
17.5.1 Impulse Approximation
17.5.2 Electron–Parton Scattering
17.6 Scattering with Equivalent Photons
17.6.1 Transverse and Longitudinal Photons
17.6.2 Spin of the Target
17.6.3 Photon Flux
17.7 How to Do Neutrino Experiments
17.7.1 Neutrino Beams
17.7.2 Neutrino Detectors
17.8 --p Deep Inelastic Scattering
17.8.1 Cross Sections and Structure Functions
17.8.2 ,--q Scattering
17.8.3 Valence Quarks and Sea Quarks
17.8.4 Comparisons with Experimental Data
17.8.5 Sum Rules
17.9 Parton Model in Hadron–Hadron Collisions
17.9.1 Drell–Yan Process
17.9.2 Other Hadronic Processes
17.10 A Glimpse of QCD's Power
18 Gauge Theories
18.1 Historical Prelude
18.2 Gauge Principle
18.2.1 Formal Definition
18.2.2 Gravity as a Geometry
18.2.3 Parallel Transport and Connection
18.2.4 Rotation in Internal Space
18.2.5 Curvature of a Space
18.2.6 Covariant Derivative
18.2.7 Principle of Equivalence
18.2.8 General Relativity and Gauge Theory
18.3 Aharonov–Bohm Effect
18.4 Nonabelian Gauge Theories
18.4.1 Isospin Operator
18.4.2 Gauge Potential
18.4.3 Isospin Force Field and Equation of Motion
18.5 QCD
18.5.1 Asymptotic Freedom
18.5.2 Confinement
18.6 Unified Theory of the Electroweak Interaction
18.6.1 SU(2)U(1) Gauge Theory
18.6.2 Spontaneous Symmetry Breaking
18.6.3 Higgs Mechanism
18.6.4 Glashow–Weinberg–Salam Electroweak Theory
18.6.5 Summary of GWS Theory
19 Epilogue
19.1 Completing the Picture
19.2 Beyond the Standard Model
19.2.1 Neutrino Oscillation
19.2.2 GUTs: Grand Unified Theories
19.2.3 Supersymmetry
19.2.4 Superstring Model
19.2.5 Extra Dimensions
19.2.6 Dark Matter
19.2.7 Dark Energy
Appendix A Spinor Representation
A.1 Definition of a Group
A.1.1 Lie Group
A.2 SU(2)
A.3 Lorentz Operator for Spin 1/2 Particle
A.3.1 SL(2,C) Group
A.3.2 Dirac Equation: Another Derivation
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 Matrices
C.2.1 Traces of the Matrices
C.2.2 Levi-Civita Antisymmetric Tensor
C.3 Spin Sum of |==========Mfi|2
C.3.1 A Frequently Used Example
C.3.2 Polarization Sum of the Vector Particle
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.1.1 Adjoint Representation
G.1.2 Direct Product
G.2 SU(3)
G.2.1 Structure Constants
G.2.2 Irreducible Representation of a Direct Product
G.2.3 Tensor Analysis
G.2.4 Young Diagram
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