An Introduction to the Standard Model of Particle Physics

Transcription

1 An Introduction to the Standard Model of Particle Physics W. N. COTTINGHAM and D. A. GREENWOOD Ж CAMBRIDGE UNIVERSITY PRESS

2 Contents Preface. page xiii Notation xv 1 The particle physicist's view of Nature Introduction The construction of the Standard Model Leptons Quarks and systems of quarks Spectroscopy of systems of light quarks More quarks Quark colour Electron scattering from nucleons Particle accelerators Units 18 2 Lorentz transformations Rotations, boosts, and proper Lorentz transformations Scalars, contravariant and covariant four-vectors Fields The Levi-Civita tensor Time reversal and space inversion 24 3 The Lagrangian formulation of mechanics Hamilton's principle Conservation of energy Continuous systems A Lorentz covariant field theory The Klein-Gordon equation 31 VII

3 viii Contents 3.6 The energy-momentum tensor Complex scalar fields 34 Classical electromagnetism Maxwell's equations A Lagrangian density for electromagnetism Gauge transformations Solutions of Maxwell's equations Space inversion Charge conjugation Intrinsic angular momentum of the photon The energy density of the electromagnetic field Massive vector fields 44 The Dirac equation and the Dirac field The Dirac equation Lorentz transformations and Lorentz invariance The parity transformation Spinors The matrices y" Making the Lagrangian density real 54 Free space solutions of the Dirac equation A Dirac particle at rest The intrinsic spin of a Dirac particle Plane waves and helicity Negative energy solutions The energy and momentum of the Dirac field The m = 0 case: the neutrino 62 Electrodynamics Probability density and probability current The Dirac equation with an electromagnetic field Gauge transformations and symmetry Charge conjugation Neutrinos and charge conjugation The electrodynamics of a charged scalar field Particles at low energies and the Dirac magnetic moment 71 Quantising fields: QED Boson and fermion field quantisation Time dependence Perturbation theory 79

4 Contents 8.4 Renormalisation and renormalisable field theories The magnetic moment of the electron Quantisation in the Standard Model 86 9 The weak interaction: low energy phenomenology Nuclear beta decay Pion decay Conservation of lepton number Muon decay The interactions of muon neutrinos with electrons Symmetry breaking in model theories Global symmetry breaking and Goldstone bosons Local symmetry breaking and the Higgs boson Massive gauge fields SU(2) symmetry The gauge fields Breaking the SU{2) symmetry Identification of the fields The Weinberg-Salam electroweak theory for leptons Lepton doublets and the Weinberg-Salam theory Lepton coupling to the W ± Lepton coupling to the Z Conservation of lepton number and conservation of charge CP symmetry Mass terms in Z : an attempted generalisation Experimental tests of the Weinberg-Salam theory The search for the gauge bosons The W 1 bosons The Z boson The number of lepton families The measurement of partial widths Left-right production cross-section asymmetry and lepton decay asymmetry of the Z boson The electromagnetic and weak interactions of quarks Construction of the Lagrangian density Quark masses and the Kobayashi-Maskawa mixing matrix The parameterisation of the KM matrix CP symmetry and the KM matrix 137

5 X Contents 14.5 The weak interaction in the low energy limit The hadronic decays of the Z and W bosons Hadronic decays of the Z Asymmetry in quark production Hadronic decays of the W* The theory of strong interactions: quantum chromodynamics A local S 1/(3) gauge theory Colour gauge transformations on baryons and mesons Lattice QCD and asymptotic freedom The quark-antiquark interaction at short distances The conservation of quarks Isospin symmetry Chiral symmetry Quantum chromodynamics: calculations Lattice QCD and confinement Charmonium and bottomonium Perturbative QCD and deep inelastic scattering Perturbative QCD and e + e~ collider physics The Kobayashi-Maskawa matrix Semileptonic weak decays F cb and K ub V ad and nuclear ß decay CP symmetry violation in neutral kaon decays CP symmetry violation in В meson decays The CPrtheorem Anomalies The Adler Bell-Jackiw anomaly Cancellation of anomalies in electroweak currents Lepton and baryon anomalies Gauge transformations and the topological number The instability of matter, and matter genesis 183 Epilogue 184 Reductionism complete? 184 Appendix A An aide-memoire on matrices 185 A.l Definitions and notation 185 A.2 Properties of и х «matrices 186

6 Contents XI A.3 Hermitian and unitary matrices 187 Appendix В The groups of the Standard Model 190 B.l Definition of a group 190 B.2 Rotations of the coordinate axes, and the group SO(3) 191 B.3 The group SU(2) 192 B.4 The group SL (2,C) and the proper Lorentz group 195 B.5 Transformations of the Pauli matrices 196 B.6 Spinors 197 B.7 The group SU(3) 198 Appendix С Annihilation and creation operators 200 C.l The simple harmonic oscillator 200 C.2 An assembly of bosons 201 C.3 An assembly of fermions 202 Appendix D The parton model 204 D.l Elastic electron scattering from nucleons 204 D.2 Inelastic electron scattering from nucleons: the parton model 205 D.3 Hadronic states 210 References 213 Hints to selected problems 215 Index 233