Introduction to Particle Physics

Description

This book focuses on the basics of particle physics, while covering as many frontier advances as possible. The book introduces readers to the principle of symmetry, properties and classification of particles, the quark model of hadrons and the interactions of particles. Following which, the book offers a step-by-step presentation on the unified theory of electromagnetic and weak interaction, as well as the gauge theory of strong interaction: quantum chromodynamics (QCD). In sequential order of the book's development, readers will study topics on the deep inelastic scattering and parton model, the mixing of electrically neutral particle and anti-particles of neutral K meson, neutral B meson and neutral D meson, the CP non-conservation, the charmonium, the exotic states, the glue-ball and hybrid state, the lattice gauge theory, the neutrino oscillation and CP violation of lepton system. Several new models beyond the standard model, such as the grand unified theory and supersymmetric model, are then discussed. As one of the salient takeaways of this book, readers will also explore the interface between cosmology and particle physics. This book is suitable for senior undergraduates, graduate students, teachers and researchers in the field of particle physics. It is also valuable for experimental and theoretical particle physicists as a foundation for further research. 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