Introduction to Particle Physics

Contents
About the Authors
Preface to the Second Edition
Preface to the First Edition
Chapter 1. Overview
References
Chapter 2. Symmetry and Conservation Law
2.1. Introduction
2.2. The Action, Equation of Motion and Conserved Quantities
2.3. Parity Transformation
2.3.1. Klein–Gordon field φ(x)
2.3.2. Parity transformation of fermion field
2.3.3. Parity transformation of vector field
2.4. Charge Conjugation
2.4.1. Charge conjugation of scalar field
2.4.2. Charge conjugation of fermion field ψ(x)
2.4.3. Charge conjugation of vector field Aμ(x)
2.5. Application: Furry Theorem — A Particle of Spin 1 Cannot Decay to 2γ
2.5.1. Furry theorem
2.5.2. Particles of spin 1 cannot decay into two photons
2.6. Time Reversal
2.6.1. Time reversal of Klein–Gordon field φ(x)
2.6.2. Time reversal of fermion field
2.6.3. Time reversal of electromagnetic field Aμ(x)
2.7. CPT Theorem
References
Chapter 3. The Classification and Properties of Particles: Lepton and Hadron
3.1. Four Types of Interactions
3.2. Lepton and Lepton Number Conservation
3.2.1. Electron, muon and neutrino
3.2.2. τ and its neutrino ντ
3.2.3. Helicity of neutrinos
3.2.4. Lepton number conservation
3.3. Hadrons: Conservation of Baryon Numbers
3.3.1. π meson
3.3.1.1. The spin of pion
3.3.1.2. The parity of pion
3.3.2. Nucleon, antinucleon and baryon number conservation
3.3.3. Strange particles
3.3.3.1. The discovery of strange particles
3.3.3.2. Associated generation and strange number
3.3.3.3. The spin and parity of strange particles
3.3.4. Resonance
3.4. Scattering Cross Section, Particle Lifetime and Decay Width
3.4.1. Scattering cross section
3.4.2. Particle lifetime and decay width
3.5. Kinematics of Particle Decay
3.5.1. Two-body decay
3.5.2. Three-body decay, Dalitz diagram
References
Chapter 4. Isospin and G Parity
4.1. Isospin
4.1.1. The concept of isospin
4.1.2. Isospin transformation
4.1.3. The law of isospin conservation in strong interaction
4.1.4. The isospin of mesons and baryons
4.1.4.1. Nucleons p and n
4.1.4.2. Isospin of π meson
4.1.4.3. The isospin of K mesosns
4.1.4.4. Isospin multiplet of other particles
4.1.5. An example of isospin analysis of physical processes
4.2. Exchange Symmetry: Generalized Identity Principle
4.3. Isospin Violation
4.4. G Parity
References
Chapter 5. Quark Model of Hadrons
5.1. Mathematical Basics
5.1.1. Decomposition of SU(n) group representation product, Young tableau
5.1.2. Tensor analysis of the SU(3) group
5.1.3. SU(3) group generators and Casmir operators
5.2. SU(3) Quark Model, the SU(3) Flavor Wave Functions for Mesons and Baryons
5.2.1. The flavor wave functions for the pseudoscalar meson octet and singlet
5.2.2. Flavor wave functions for the vector meson octet and singlet
5.2.3. Flavor wave functions for baryon octet and decuplet
5.3. Color Degree of Freedom
5.3.1. The relationship of baryon spin and statistics
5.3.2. π0 →γγ
5.3.3. Measurement of R value in e+e− annihilation process
5.4. Mass Formula of Hadrons
5.5. Mixing of Meson Singlet and Octet
5.6. OZI Rule
5.7. SU(6) Symmetry
5.8. Orbital Excitation States and Radial Excitation States, Multi-quark States and Exotic States
5.8.1. Orbital and radial excitation states
5.8.2. Multi-quark states and exotic states
5.9. The Discovery of c, b, t Quarks
5.10. Quark Confinement
References
Chapter 6. Electromagnetic Interaction
6.1. QED and Its Feynman Rule
6.2. Møller Scattering
6.3. Bhabha Scattering
6.4. The Electromagnetic Form Factors of Nucleons
6.4.1. Electron–proton elastic scattering assuming proton being a point-like particle
6.4.2. Elastic scattering of electron–proton
6.5. Inelastic Scattering of Electron–Proton
6.5.1. Structure function of inelastic scattering
6.5.2. The structure function applied to elastic scattering
6.6. The Parton Model for Nucleons
6.7. The Unification of Parton and Quark Model
References
Chapter 7. Weak Interactions
7.1. Looking Back to History
7.2. Classification of Weak Decays
7.3. Nuclear β Decay
7.4. The Discovery of Parity Violation
7.4.1. τ–θ Puzzle
7.4.2. Parity violation in β decays of cobalt 60 nuclei
7.5. The V–A Theory of Weak Interactions
7.5.1. Pure leptonic decay
7.5.2. Semi-leptonic decay
7.6. Cabibbo Theory and GIM Mechanism
7.7. Kobayashi–Maskawa Model
7.8. The Limitation of the Four Fermion Point-like Interactions and the Intermediate Vector Bosons
7.9. Conservation of Vector Current
7.10. Chiral Symmetry Breaking and PCAC
7.11. Mixing of Neutral Mesons and CP Violation
7.11.1. Quantum mechanical description
7.11.2. K0–K0 mixing and CP violation
7.11.2.1. K0–K0 mixing
7.11.2.2. Reproduction of neutral K meson
7.11.2.3. Discovery of CP violation
7.11.2.4. Isospin description of K0 → 2π decays
7.11.2.5. CP violation in K0 → 3π decays
7.11.2.6. The relation of ε and ε
7.11.3. B0–B0 mixing and CP violation
7.11.3.1. Experimental measurements of B0d–B0d mixing
7.11.3.2. Theoretical calculation of the mixing parameter x
7.11.3.3. B meson factory
7.11.3.4. CP violation in B meson system
7.11.3.5. Unitarity triangle
7.11.4. D0–D0 mixing and CP violation
7.11.4.1. Theoretical prediction for D0–D0 mixing
7.11.4.2. Experimental measurements for D0–D0 mixing parameters
7.11.4.3. Direct CP violation in charmed particles
References
Chapter 8. Gauge Theory of Electroweak Unification
8.1. The Higgs Mechanism
8.2. Yang–Mills Theory
8.3. Glashow–Weinberg–Salam Electroweak Unification Model
8.4. The Vacuum Spontaneous Symmetry Breaking: The Higgs Mechanism
8.4.1. The kinetic energy, mass and self-interaction term of scalar field
8.4.2. The mass term of gauge field
8.4.3. The interaction term of the scalar and gauge fields
8.5. The Gain of the Fermion Mass: Yukawa Coupling
8.6. The Interaction of Fermion and Gauge Field II
8.7. The Interaction of Gauge Fields
8.8. Feynman Rule in the Renormalization Gauge (Rξ Gauge)
8.8.1. For pure scalar field
8.8.2. For the interaction of scalar and gauge fields
8.8.3. For ghost fields
8.8.4. The kinetic energy term of the Lagrangian in Rξ gauge
8.8.5. The interaction terms of scalar and fermions
8.9. The Discovery of Higgs Boson
References
Chapter 9. Theory of Strong Interaction: QCD
9.1. The SU(3) Gauge Symmetry of Color
9.2. The Quantization of Gauge Field and Fermion Field
9.2.1. The path integral quantization
9.2.2. Reduction formula
9.2.3. The quantization of gauge field
9.2.4. The quantization of fermion field and Grassmann algebra
9.3. The Effective Lagrangian of QCD and Perturbation Theory
9.3.1. The effective Lagrangian of QCD
9.3.2. Perturbation expansion
9.3.2.1. The perturbative expansion of ϕ3 theory
9.3.2.2. The perturbative expansion of QCD and Feynman rule
9.4. Divergence and Regularization of Loop Corrections
9.5. The Renormalization of Divergence
9.5.1. The superficial degree of divergence
9.5.2. The renormalizability of a theory
9.5.3. The renormalization of QCD
9.5.3.1. On-shell subtraction
9.5.3.2. Off-shell subtraction
9.5.3.3. The minimum subtraction scheme
9.5.3.4. The modified minimum subtraction scheme
9.5.4. One-loop result of the renormalization constants
9.5.4.1. The gluon self-energy part
9.5.4.2. The self-energy of ghost field
9.5.4.3. The quark self-energy
9.5.4.4. The three-gluon vertex
9.5.4.5. The four-gluon vertex
9.5.4.6. The ghost–gluon interaction vertex
9.5.4.7. The quark–gluon vertex
9.6. BRST Symmetry and the Generalized Ward–Takahashi Identity
9.6.1. BRST symmetry
9.6.2. The generalized Ward–Takahashi identity (Slavnov–Taylor identity)
9.7. The Renormalization Group Equation and the Solution
9.7.1. The renormalization group
9.7.1.1. The finite renormalization of the coupling constant
9.7.1.2. The finite renormalization of quark mass
9.7.1.3. The finite renormalization of green function
9.7.2. The renormalization group equations
9.7.3. The solution of the renormalization group equation
9.8. Asymptotic Freedom
9.9. Structure Function, Parton Distribution Function and the Application in Perturbative QCD
9.9.1. Structural function of deep inelastic scattering process
9.9.2. The prediction of QCD to the variation of structure function with Q2
9.9.3. Examples for application
9.10. A Brief Introduction to Some Bound States in QCD
9.10.1. e+e− collision, charmonium and bottomonium
9.10.2. Glueball and hybrid state
9.11. Nonperturbative QCD and Lattice Gauge Theory
9.12. The Strong CP Problem
References
Chapter 10. Neutrino Oscillation
10.1. Experimental Evidence for Neutrino Oscillation
10.1.1. Atmospheric neutrino oscillation
10.1.2. Accelerator neutrino oscillation
10.1.3. Solar neutrino oscillation
10.1.4. Reactor neutrino oscillation
10.2. Theoretical Description of Neutrino Oscillation
10.2.1. Neutrino oscillation in vacuum
10.2.2. Neutrino oscillation in matter
10.3. Dirac Neutrino and Majorana Neutrino
10.3.1. Dirac neutrino
10.3.2. Majorana neutrino
10.4. Neutrino Mass and See-Saw Mechanism
10.5. Parameterization of Neutrino Mixing Matrix
10.6. CP Violation in Neutrino Oscillation
10.7. Neutrino Mass Hierarchy Problem
10.8. Perspectives
References
Chapter 11. Beyond Standard Model
11.1. Grand Unified Theories for Strong, Electromagnetic and Weak Interactions
11.1.1. SU(5) grand unified theory
11.1.1.1. Adler anomaly of SU(N) group representation
11.1.1.2. Filling representations for fermions and gauge bosons in the SU(5) grand unified model
11.1.1.3. Higgs mechanism
11.1.1.4. Fermion masses
11.1.1.5. Masses of gauge bosons
11.1.1.6. Proton decay
11.1.2. SO(2N) grand unified models
11.1.3. Flavor unification
11.2. Supersymmetric Models
11.2.1. Superspace and superfields
11.2.2. Global supersymmetry and local supersymmetry (Supergravity)
11.2.3. Global supersymmetric theory and minimal supersymmetric standard model
11.2.3.1. Scalar (chiral) superfield and vector superfield
11.2.3.2. Constructing lagrangian
11.2.3.3. Minimal supersymmetric standard model
11.3. Superstring Theory and Brane Theory
References
Chapter 12. Particle Physics and Cosmology
12.1. Basics of the Big Bang ΛCDM Model
12.1.1. Hubble’s law
12.1.2. The Robertson–Walker metric and the Friedmann equation
12.1.3. Definitions of some cosmological parameters
12.1.4. The redshift and its relation with the physical distance
12.1.5. Some important solutions to the standard ΛCDM model
12.1.5.1. The solutions based on a specific equation of state
12.1.5.2. The solutions of the standard model of the Universe for the epoch dominated by radiation
12.1.5.3. The solutions of the standard model of the Universe for the epoch dominated by matter
12.1.5.4. The solutions of the standard model of the Universe for the epoch dominated by vacuum energy
12.1.6. The age of the Universe
12.2. Hot Big Bang and Radiation in the Early Universe
12.3. Neutrino Decoupling and Cosmic Neutrino Background
12.4. Big Bang Nucleosynthesis and Abundances of Primordial Light Elements
12.5. Cosmological Baryon–Antibaryon Asymmetry
12.6. Dark Matter
12.7. Dark Energy
12.8. Cosmic Microwave Background
12.8.1. Transition of the Universe to its matter-dominated epoch
12.8.2. Formation of the CMB
12.8.3. Anisotropies of the CMB
12.9. Three Cosmic Problems and the Inflation Mechanism
12.9.1. Three problems in cosmology
12.9.1.1. The horizon problem
12.9.1.2. The flatness problem
12.9.1.3. The magnetic monopole problem
12.9.2. The inflation mechanism
12.9.2.1. A solution to the flatness problem
12.9.2.2. A solution to the horizon problem
12.9.2.3. A solution to the magnetic monopole problem
References
Chapter 13. Epilogue
Unsolved Ten Problems
Appendix I. Calculation of Some Cross Sections
I.1. Calculation of the Cross Section of Electron–Proton Elastic Scattering with Proton Being Viewed as a Point Particle
I.2. Calculation of the Elastic Scattering Cross Section of Electron and a Particle with Spin 0 and Charge 1
I.3. Calculation of the Cross Section of Electron–Proton Elastic Scattering
I.4. Calculation of the Cross Section of Eectron–Proton Inelastic Scattering
I.5. Calculation of the Differential Cross Section of Electron–Parton Scattering
I.6. Calculation of the Cross Section of Neutrino–Lepton Scattering in the Theory of Four-Fermion Point-Interaction
Appendix II. Table of Physical Constants
References
Index