Gauge Theories in Particle Physics: A Practical Introduction, Volume 2: Non-Abelian Gauge Theories : QCD and The Electroweak Theory, Fourth Edition

The fourth edition of this well-established, highly regarded two-volume set continues to provide a fundamental introduction to advanced particle physics while incorporating substantial new experimental results, especially in the areas of CP violation and neutrino oscillations. It offers an accessible and practical introduction to the three gauge theories included in the Standard Model of particle physics: quantum electrodynamics (QED), quantum chromodynamics (QCD), and the Glashow-Salam-Weinberg (GSW) electroweak theory. In the first volume, a new chapter on Lorentz transformations and discrete symmetries presents a simple treatment of Lorentz transformations of Dirac spinors. Along with updating experimental results, this edition also introduces Majorana fermions at an early stage, making the material suitable for a first course in relativistic quantum mechanics. Covering much of the experimental progress made in the last ten years, the second volume remains focused on the two non-Abelian quantum gauge field theories of the Standard Model: QCD and the GSW electroweak theory. A new chapter on CP violation and oscillation phenomena describes CP violation in B-meson decays as well as the main experiments that have led to our current knowledge of mass-squared differences and mixing angles for neutrinos. Exploring a new era in particle physics, this edition discusses the exciting discovery of a boson with properties consistent with those of the Standard Model Higgs boson. It also updates many other topics, including jet algorithms, lattice QCD, effective Lagrangians, and three-generation quark mixing and the CKM matrix. This revised and updated edition provides a self-contained pedagogical treatment of the subject, from relativistic quantum mechanics to the frontiers of the Standard Model. For each theory, the authors discuss the main conceptual points, detail many practical calculations of physical quantities from first principles, and compare these quantitative predictions with experimental results, helping readers improve both their calculation skills and physical insight. Cover Volume 1 Cover Half Title Title Page Copyright Page Dedication Page Contents Preface I Introductory Survey, Electromagnetism as a Gauge Theory, and Relativistic Quantum Mechanics 1 The Particles and Forces of the Standard Model 1.1 Introduction: the Standard Model 1.2 The fermions of the Standard Model 1.2.1 Leptons 1.2.2 Quarks 1.3 Particle interactions in the Standard Model 1.3.1 Classical and quantum fields 1.3.2 The Yukawa theory of force as virtual quantum exchange 1.3.3 The one-quantum exchange amplitude 1.3.4 Electromagnetic interactions 1.3.5 Weak interactions 1.3.6 Strong interactions 1.3.7 The gauge bosons of the Standard Model 1.4 Renormalization and the Higgs sector of the Standard Model 1.4.1 Renormalization 1.4.2 The Higgs boson of the Standard Model 1.5 Summary Problems 2 Electromagnetism as a Gauge Theory 2.1 Introduction 2.2 The Maxwell equations: current conservation 2.3 The Maxwell equations: Lorentz covariance and gauge invariance 2.4 Gauge invariance (and covariance) in quantum mechanics 2.5 The argument reversed: the gauge principle 2.6 Comments on the gauge principle in electromagnetism Problems 3 Relativistic Quantum Mechanics 3.1 The Klein–Gordon equation 3.1.1 Solutions in coordinate space 3.1.2 Probability current for the KG equation 3.2 The Dirac equation 3.2.1 Free-particle solutions 3.2.2 Probability current for the Dirac equation 3.3 Spin 3.4 The negative-energy solutions 3.4.1 Positive-energy spinors 3.4.2 Negative-energy spinors 3.4.3 Dirac’s interpretation of the negative-energy solutions of the Dirac equation 3.4.4 Feynman’s interpretation of the negative-energy solutions of the KG and Dirac equations 3.5 Inclusion of electromagnetic interactions via the gauge principle: the Dirac prediction of g = 2 for the electron Problems 4 Lorentz Transformations and Discrete Symmetries 4.1 Lorentz transformations 4.1.1 The KG equation 4.1.2 The Dirac equation 4.2 Discrete transformations: P, C and T 4.2.1 Parity 4.2.2 Charge conjugation 4.2.3 CP 4.2.4 Time reversal 4.2.5 CPT Problems II Introduction to Quantum Field Theory 5 Quantum Field Theory I: The Free Scalar Field 5.1 The quantum field: (i) descriptive 5.2 The quantum field: (ii) Lagrange–Hamilton formulation 5.2.1 The action principle: Lagrangian particle mechanics 5.2.2 Quantum particle mechanics à la Heisenberg–Lagrange–Hamilton 5.2.3 Interlude: the quantum oscillator 5.2.4 Lagrange–Hamilton classical field mechanics 5.2.5 Heisenberg–Lagrange–Hamilton quantum field mechanics 5.3 Generalizations: four dimensions, relativity and mass Problems 6 Quantum Field Theory II: Interacting Scalar Fields 6.1 Interactions in quantum field theory: qualitative introduction 6.2 Perturbation theory for interacting fields: the Dyson expansion of the S-matrix 6.2.1 The interaction picture 6.2.2 The S-matrix and the Dyson expansion 6.3 Applications to the ‘ABC’ theory 6.3.1 The decay C →A + B 6.3.2 A + B → A + B scattering: the amplitudes 6.3.3 A + B → A + B scattering: the Yukawa exchange mechanism, s and u channel processes 6.3.4 A + B → A + B scattering: the differential cross section 6.3.5 A + B → A + B scattering: loose ends Problems 7 Quantum Field Theory III: Complex Scalar Fields, Dirac and Maxwell Fields; Introduction of Electromagnetic Interactions 7.1 The complex scalar field: global U(1) phase invariance, particles and antiparticles 7.2 The Dirac field and the spin-statistics connection 7.3 The Maxwell field Aμ(x) 7.3.1 The classical field case 7.3.2 Quantizing Aμ(x) 7.4 Introduction of electromagnetic interactions 7.5 P, C and T in quantum field theory 7.5.1 Parity 7.5.2 Charge conjugation 7.5.3 Time reversal Problems III Tree-Level Applications in QED 8 Elementary Processes in Scalar and Spinor Electrodynamics 8.1 Coulomb scattering of charged spin-0 particles 8.1.1 Coulomb scattering of s+ (wavefunction approach) 8.1.2 Coulomb scattering of s+ (field-theoretic approach) 8.1.3 Coulomb scattering of s− 8.2 Coulomb scattering of charged spin-1⁄2 particles 8.2.1 Coulomb scattering of e− (wavefunction approach) 8.2.2 Coulomb scattering of e−(field-theoretic approach) 8.2.3 Trace techniques for spin summations 8.2.4 Coulomb scattering of e+ 8.3 e−s+ scattering 8.3.1 The amplitude for e−s+ → e−s+ 8.3.2 The cross section for e−s+ → e−s+ 8.4 Scattering from a non-point-like object: the pion form factor in e−π+ → e−π+ 8.4.1 e− scattering from a charge distribution 8.4.2 Lorentz invariance 8.4.3 Current conservation 8.5 The form factor in the time-like region: e+e− → π+π− and crossing symmetry 8.6 Electron Compton scattering 8.6.1 The lowest-order amplitudes 8.6.2 Gauge invariance 8.6.3 The Compton cross section 8.7 Electronmuon elastic scattering 8.8 Electron–proton elastic scattering and nucleon form factors 8.8.1 Lorentz invariance 8.8.2 Current conservation Problems 9 Deep Inelastic Electron–Nucleon Scattering and the Parton Model 9.1 Inelastic electron–proton scattering: kinematics and structure functions 9.2 Bjorken scaling and the parton model 9.3 Partons as quarks and gluons 9.4 The Drell–Yan process 9.5 e+e− annihilation into hadrons Problems IV Loops and Renormalization 10 Loops and Renormalization I: The ABC Theory 10.1 The propagator correction in ABC theory 10.1.1 The O(g2) self-energy ∏[2]C (q2) 10.1.2 Mass shift 10.1.3 Field strength renormalization 10.2 The vertex correction 10.3 Dealing with the bad news: a simple example 10.3.1 Evaluating ∏[2]C (q2) 10.3.2 Regularization and renormalization 10.4 Bare and renormalized perturbation theory 10.4.1 Reorganizing perturbation theory 10.4.2 The O(g2ph) renormalized self-energy revisited: how counter terms are determined by renormalization conditions 10.5 Renormalizability Problems 11 Loops and Renormalization II: QED 11.1 Counter terms 11.2 The O(e2) fermion self-energy 11.3 The O(e2) photon self-energy 11.4 The O(e2) renormalized photon self-energy 11.5 The physics of ∏̅γ[2] (q2) 11.5.1 Modified Coulomb’s law 11.5.2 Radiatively induced charge form factor 11.5.3 The running coupling constant 11.5.4 ∏̅γ[2] in the s-channel 11.6 The O(e2) vertex correction, and Z1 = Z2 11.7 The anomalous magnetic moment and tests of QED 11.8 Which theories are renormalizable – and does it matter? Problems A Non-relativistic Quantum Mechanics B Natural Units C Maxwell’s Equations: Choice of Units D Special Relativity: Invariance and Covariance E Dirac δ-Function F Contour Integration G Green Functions H Elements of Non-relativistic Scattering Theory H.1 Time-independent formulation and differential cross section H.2 Expression for the scattering amplitude: Born approximation H.3 Time-dependent approach I The Schrödinger and Heisenberg Pictures J Dirac Algebra and Trace Identities J.1 Dirac algebra J.1.1 γ matrices J.1.2 γ5 identities J.1.3 Hermitian conjugate of spinor matrix elements J.1.4 Spin sums and projection operators J.2 Trace theorems K Example of a Cross Section Calculation K.1 The spin-averaged squared matrix element K.2 Evaluation of two-body Lorentz-invariant phase space in ‘laboratory’ variables L Feynman Rules for Tree Graphs in QED L.1 External particles L.2 Propagators L.3 Vertices References Index Volume 2 Cover Half Title Title Page Copyright Page Dedication Page Contents Preface V Non-Abelian Symmetries 12 Global Non-Abelian Symmetries 12.1 The Standard Model 12.2 The flavour symmetry SU(2)f 12.2.1 The nucleon isospin doublet and the group SU(2) 12.2.2 Larger (higher-dimensional) multiplets of SU(2) in nuclear physics 12.2.3 Isospin in particle physics: flavour SU(2)f 12.3 Flavour SU(3)f 12.4 Non-Abelian global symmetries in Lagrangian quantum field theory 12.4.1 SU(2)f and SU(3)f 12.4.2 Chiral symmetry Problems 13 Local Non-Abelian (Gauge) Symmetries 13.1 Local SU(2) symmetry 13.1.1 The covariant derivative and interactions with matter 13.1.2 The non-Abelian field strength tensor 13.2 Local SU(3) Symmetry 13.3 Local non-Abelian symmetries in Lagrangian quantum field theory 13.3.1 Local SU(2) and SU(3) Lagrangians 13.3.2 Gauge field self-interactions 13.3.3 Quantizing non-Abelian gauge fields Problems VI QCD and the Renormalization Group 14 QCD I: Introduction, Tree Graph Predictions, and Jets 14.1 The colour degree of freedom 14.2 The dynamics of colour 14.2.1 Colour as an SU(3) group 14.2.2 Global SU(3)c invariance, and ‘scalar gluons’ 14.2.3 Local SU(3)c invariance: the QCD Lagrangian 14.2.4 The θ-term 14.3 Hard scattering processes, QCD tree graphs, and jets 14.3.1 Introduction 14.3.2 Two-jet events in p̅p collisions 14.3.3 Three-jet events in p̅p collisions 14.4 3-jet events in e+e− annihilation 14.4.1 Calculation of the parton-level cross section 14.4.2 Soft and collinear divergences 14.5 Definition of the two-jet cross section in e+e− annihilation 14.6 Further developments 14.6.1 Test of non-Abelian nature of QCD in e+e− → 4 jets 14.6.2 Jet algorithms Problems 15 QCD II: Asymptotic Freedom, the Renormalization Group, and Scaling Violations 15.1 Higher-order QCD corrections to σ(e+e− → hadrons): large logarithms 15.2 The renormalization group and related ideas in QED 15.2.1 Where do the large logs come from? 15.2.2 Changing the renormalization scale 15.2.3 The RGE and large −q2 behaviour in QED 15.3 Back to QCD: asymptotic freedom 15.3.1 One loop calculation 15.3.2 Higher-order calculations, and experimental comparison 15.4 σ(e+e− → hadrons) revisited 15.5 A more general form of the RGE: anomalous dimensions and running masses 15.6 QCD corrections to the parton model predictions for deep inelastic scattering: scaling violations 15.6.1 Uncancelled mass singularities at order αs 15.6.2 Factorization, and the order αs DGLAP equation 15.6.3 Comparison with experiment Problems 16 Lattice Field Theory, and the Renormalization Group Revisited 16.1 Introduction 16.2 Discretization 16.2.1 Scalar fields 16.2.2 Dirac fields 16.2.3 Gauge fields 16.3 Representation of quantum amplitudes 16.3.1 Quantum mechanics 16.3.2 Quantum field theory 16.3.3 Connection with statistical mechanics 16.4 Renormalization, and the renormalization group, on the lattice 16.4.1 Introduction 16.4.2 Two one-dimensional examples 16.4.3 Connections with particle physics 16.5 Lattice QCD 16.5.1 Introduction, and the continuum limit 16.5.2 The static qq̅ potential 16.5.3 Calculation of α(M2Z) 16.5.4 Hadron masses Problems VII Spontaneously Broken Symmetry 17 Spontaneously Broken Global Symmetry 17.1 Introduction 17.2 The Fabri–Picasso theorem 17.3 Spontaneously broken symmetry in condensed matter physics 17.3.1 The ferromagnet 17.3.2 The Bogoliubov superfluid 17.4 Goldstone’s theorem 17.5 Spontaneously broken global U(1) symmetry: the Goldstone model 17.6 Spontaneously broken global non-Abelian symmetry 17.7 The BCS superconducting ground state Problems 18 Chiral Symmetry Breaking 18.1 The Nambu analogy 18.1.1 Two flavour QCD and SU(2)f L×SU(2)f R 18.2 Pion decay and the Goldberger–Treiman relation 18.3 Effective Lagrangians 18.3.1 The linear and non-linear σ-models 18.3.2 Inclusion of explicit symmetry breaking: masses for pions and quarks 18.3.3 Extension to SU(3)f L×SU(3)f R 18.4 Chiral anomalies Problems 19 Spontaneously Broken Local Symmetry 19.1 Massive and massless vector particles 19.2 The generation of ‘photon mass’ in a superconductor: Ginzburg–Landau theory and the Meissner effect 19.3 Spontaneously broken local U(1) symmetry: the Abelian Higgs model 19.4 Flux quantization in a superconductor 19.5 ’t Hooft’s gauges 19.6 Spontaneously broken local SU(2) × U(1) symmetry Problems VIII Weak Interactions and the Electroweak Theory 20 Introduction to the Phenomenology of Weak Interactions 20.1 Fermi’s ‘current–current’ theory of nuclear β-decay, and its generalizations 20.2 Parity violation in weak interactions, and V-A theory 20.2.1 Parity violation 20.2.2 V-A theory: chirality and helicity 20.3 Lepton number and lepton flavours 20.4 The universal current × current theory for weak interactions of leptons 20.5 Calculation of the cross section for νμ + e− → μ− + νe 20.6 Leptonic weak neutral currents 20.7 Quark weak currents 20.7.1 Two generations 20.7.2 Deep inelastic neutrino scattering 20.7.3 Three generations 20.8 Non-leptonic weak interactions Problems 21 CP Violation and Oscillation Phenomena 21.1 Direct CP violation in B decays 21.2 CP violation in B meson oscillations 21.2.1 Time-dependent mixing formalism 21.2.2 Determination of the angles α(φ2) and β(φ1) of the unitarity triangle 21.3 CP violation in neutral K-meson decays 21.4 Neutrino mixing and oscillations 21.4.1 Neutrino mass and mixing 21.4.2 Neutrino oscillations: formulae 21.4.3 Neutrino oscillations: experimental results 21.4.4 Matter effects in neutrino oscillations 21.4.5 Further developments Problems 22 The Glashow–Salam–Weinberg Gauge Theory of Electroweak Interactions 22.1 Difficulties with the current–current and ‘naive’ IVB models 22.1.1 Violations of unitarity 22.1.2 The problem of non-renormalizability in weak interactions 22.2 The SU(2) × U(1) electroweak gauge theory 22.2.1 Quantum number assignments; Higgs, W and Z masses 22.2.2 The leptonic currents (massless neutrinos): relation to current–current model 22.2.3 The quark currents 22.3 Simple (tree-level) predictions 22.4 The discovery of the W± and Z0 at the CERN pp̅ collider 22.4.1 Production cross sections for W and Z in pp̅ colliders 22.4.2 Charge asymmetry in W± decay 22.4.3 Discovery of theW± and Z0 at the pp̅ collider, and their properties 22.5 Fermion masses 22.5.1 One generation 22.5.2 Three-generation mixing 22.6 Higher-order corrections 22.7 The top quark 22.8 The Higgs sector 22.8.1 Introduction 22.8.2 Theoretical considerations concerning mH 22.8.3 Higgs boson searches and the 2012 discovery Problems M Group Theory M.1 Definition and simple examples M.2 Lie groups M.3 Generators of Lie groups M.4 Examples M.4.1 SO(3) and three-dimensional rotations M.4.2 SU(2) M.4.3 SO(4): The special orthogonal group in four dimensions M.4.4 The Lorentz group M.4.5 SU(3) M.5 Matrix representations of generators, and of Lie groups M.6 The Lorentz group M.7 The relation between SU(2) and SO(3) N Geometrical Aspects of Gauge Fields N.1 Covariant derivatives and coordinate transformations N.2 Geometrical curvature and the gauge field strength tensor O Dimensional Regularization P Grassmann Variables Q Feynman Rules for Tree Graphs in QCD and the Electroweak Theory Q.1 QCD Q.1.1 External particles Q.1.2 Propagators Q.1.3 Vertices Q.2 The electroweak theory Q.2.1 External particles Q.2.2 Propagators Q.2.3 Vertices References Index "The first volume of this updated fourth edition includes self-contained presentations of electromagnetism as a gauge theory as well as relativistic quantum mechanics. It provides a unique elementary introduction to quantum field theory, establishing the essentials of the formal and conceptual framework upon which the subsequent development of the three gauge theories is based. The text also describes tree-level calculations of physical processes in QED and introduces ideas of renormalization in the context of one-loop radiative corrections for QED"-- Provided by publisher