Particle Physics

Professor Brian R Martin, Emeritus, Department of Physics & Astronomy, University College London, UKBrian Martin was a full-time member of staff of the Department of Physics & Astronomy at UCL from 1968 to 1995, including a decade from 1994 to 2004 as Head of the Department. He retired in 2005 and now holds the title of Emeritus Professor of Physics. He has extensive experience of teaching undergraduate mathematics classes at all levels and experience of other universities via external examining for first degrees at Imperial College and Royal Holloway College London. He was also the external member of the General Board of the Department of Physics at Cambridge University that reviewed the whole academic programme of that department, including teaching.Dr Graham Shaw, School of Physics & Astronomy, The University of Manchester, UKGraham Shaw (http://www.hep.man.ac.uk/u/graham/) was a full-time member of staff of the School of Physics & Astronomy at Manchester University until September 2009. He continued to teach part-time until September 2012 and currently holds an honorary position in the department. He has extensive experience of teaching undergraduate physics and the associated mathematics and was a member of the school's Teaching Committee and Course Director of the Honours School of Mathematics and Physics for many years.

• Editors’ preface to the Manchester Physics Series xiiiAuthors’ preface xvSuggested Short Course xviiNotes xixPhysical  Constants,  Conversion  Factors  and Natural Units xxi1 Some basic concepts 11.1 Introduction 11.2 Antiparticles 31.2.1 Relativistic wave equations 31.2.2 Hole theory and the positron 61.3 Interactions and Feynman diagrams 91.3.1 Basic electromagnetic processes 101.3.2 Real processes 111.3.3 Electron–positron pair production and annihilation 131.3.4 Other processes 151.4 Particle exchange 151.4.1 Range of forces 151.4.2 The Yukawa potential 171.4.3 The zero-range approximation 181.5 Units and dimensions 19Problems 1 222 Leptons and the weak interaction 242.1 Lepton multiplets and lepton numbers 242.1.1 Electron neutrinos 252.1.2 Further generations 282.2 Leptonic weak interactions 312.2.1 W± and Z0 exchange 312.2.2 Lepton decays and universality 332.3 Neutrino masses and neutrino mixing 352.3.1 Neutrino mixing 352.3.2 Neutrino oscillations 382.3.3 Neutrino masses 462.3.4 Lepton numbers revisited 48Problems 2 503 Quarks and hadrons 523.1 Quarks 533.2 General properties of hadrons 553.3 Pions and nucleons 583.4 Strange particles, charm and bottom 613.5 Short-lived hadrons 663.6 Allowed and exotic quantum numbers 72Problems 3 754 Experimental methods 774.1 Overview 774.2 Accelerators and beams 794.2.1 Linear accelerators 804.2.2 Cyclic accelerators 814.2.3 Fixed-target machines and colliders 834.2.4 Neutral and unstable particle beams 854.3 Particle interactions with matter 864.3.1 Short-range interactions with nuclei 864.3.2 Ionisation energy losses 894.3.3 Radiation energy losses 924.3.4 Interactions of photons in matter 934.3.5 Ranges and interaction lengths 944.4 Particle detectors 954.4.1 Introduction 964.4.2 Gaseous ionisation detectors 974.4.3 Semiconductor detectors 1034.4.4 Scintillation counters 1044.4.5 ˇCerenkov counters and transition radiation 1054.4.6 Calorimeters 1094.5 Detector systems and accelerator experiments 1124.5.1 Discovery of the W± and Z0 bosons 1134.5.2 Some modern detector systems 1174.6 Non-accelerator experiments 121Problems 4 1235 Space–time symmetries 1265.1 Translational invariance 1275.2 Rotational invariance 1295.2.1 Angular momentum conservation 1295.2.2 Classification of particles 1325.2.3 Angular momentum in the quark model 1345.3 Parity 1355.3.1 Leptons and antileptons 1375.3.2 Quarks and hadrons 1395.3.3 Parity of the charged pion 1405.3.4 Parity of the photon 1415.4 Charge conjugation 1425.4.1 π0 and η decays 1445.5 Positronium 1455.5.1 Fine structure 1475.5.2 C-parity and annihilations 1485.6 Time reversal 1495.6.1 Principle of detailed balance 1515.6.2 Spin of the charged pion 152Problems 5 1536 The quark model 1556.1 Isospin symmetry 1566.1.1 Isospin quantum numbers 1576.1.2 Allowed quantum numbers 1586.1.3 An example: the sigma (Σ) baryons 1596.1.4 The u, d quark mass splitting 1616.2 The lightest hadrons 1626.2.1 The light mesons 1626.2.2 The light baryons 1646.2.3 Baryon magnetic moments 1676.2.4 Hadron mass splittings 1696.3 The L = 0 heavy quark states 1746.4 Colour 1776.4.1 Colour charges and confinement 1786.4.2 Colour wavefunctions and the Pauli principle 1826.5 Charmonium and bottomonium 1846.5.1 Charmonium 1856.5.2 Bottomonium 1896.5.3 The quark–antiquark potential 189Problems 6 1917 QCD, jets and gluons 1937.1 Quantum chromodynamics 1937.1.1 The strong coupling constant 1977.1.2 Screening, antiscreening and asymptotic freedom 1997.1.3 Exotic hadrons 2017.1.4 The quark–gluon plasma 2087.2 Electron–positron annihilation 2107.2.1 Two-jet events 2117.2.2 Three-jet events 2137.2.3 The total cross-section 214Problems 7 2158 Quarks and partons 2178.1 Elastic electron scattering: the size of the proton 2178.1.1 Static charge distributions 2188.1.2 Proton form factors 2198.1.3 The basic cross-section formulas 2218.2 Inelastic electron and muon scattering 2228.2.1 Bjorken scaling 2248.2.2 The parton model 2268.2.3 Parton distributions and scaling violations 2288.3 Inelastic neutrino scattering 2318.3.1 Quark identification and quark charges 2348.4 Other processes 2368.4.1 Lepton pair production 2398.4.2 Jets in pp collisions 2428.5 Current and constituent quarks 243Problems 8 2469 Weak interactions: quarks and leptons 2489.1 Charged current reactions 2509.1.1 W±–lepton interactions 2509.1.2 Lepton–quark symmetry and mixing 2549.1.3 W boson decays 2589.1.4 Selection rules in weak decays 2599.2 The third generation 2629.2.1 More quark mixing 2639.2.2 Properties of the top quark 2659.2.3 Discovery of the top quark 267Problems 9 27410 Weak interactions: electroweak unification 27610.1 Neutral currents and the unified theory 27710.1.1 The basic vertices 27710.1.2 The unification condition and the W± and Z0 masses 27910.1.3 Electroweak reactions 28110.1.4 Z0 formation: how many generations are there? 28410.2 Gauge invariance and the Higgs boson 28710.2.1 Unification and the gauge principle 28910.2.2 Particle masses and the Higgs field 29010.2.3 Properties of the Higgs boson 29410.2.4 The discovery of the Higgs boson 297Problems 10 30511 Discrete symmetries: C, P, CP and CPT 30811.1 P violation, C violation and CP conservation 30811.1.1 Muon decay symmetries 31011.1.2 Left-handed neutrinos and right-handed antineutrinos 31211.1.3 Pion and muon decays revisited 31411.2 CP violation and particle–antiparticle mixing 31611.2.1 CP eigenstates of neutral kaons 31611.2.2 The discovery of CP violation 31911.2.3 CP-violating K0L decays 32111.2.4 Flavour oscillations and the CPT theorem 32411.2.5 Direct CP violation in decay rates 32811.2.6 B0 − B0 mixing 32911.2.7 CP violation in interference 33511.2.8 Derivation of the mixing formulas 33811.3 CP violation in the standard model 340Problems 11 34312 Beyond the standard model 34612.1 Grand unification 34712.1.1 Quark and lepton charges 34912.1.2 The weak mixing angle 34912.1.3 Proton decay 35012.2 Supersymmetry 35412.2.1 The search for supersymmetry 35612.3 Strings and things 35812.4 Particle physics and cosmology 36012.4.1 Dark matter 36012.4.2 Matter–antimatter asymmetry 36712.4.3 CP violation and electric dipole moments 36912.4.4 Axions and the strong CP problem 37112.5 Dirac or Majorana neutrinos? 37312.5.1 Double beta decay 375Problems 12 381A Relativistic kinematics 383A.1 The Lorentz transformation for energy and momentum 383A.2 The invariant mass 385A.2.1 Beam energies and thresholds 385A.2.2 Masses of unstable particles 387A.3 Transformation of the scattering angle 388Problems A 390B Amplitudes and cross-sections 392B.1 Rates and cross-sections 392B.2 The total cross-section 394B.3 Differential cross-sections 395B.4 The scattering amplitude 397B.5 The Breit–Wigner formula 400B.5.1 Decay distributions 401B.5.2 Resonant cross-sections 404Problems B 406C The isospin formalism 408C.1 Isospin operators 409C.2 Isospin states 411C.3 Isospin multiplets 411C.3.1 Hadron states 412C.4 Branching ratios 414C.5 Spin states 416Problems C 416D Gauge theories 418D.1 Electromagnetic interactions 419D.2 Gauge transformations 420D.3 Gauge invariance and the photon mass 421D.4 The gauge principle 423D.5 The Higgs mechanism 425D.5.1 Charge and current densities 425D.5.2 Spin-0 bosons 427D.5.3 Spontaneous symmetry breaking 428D.6 Quantum chromodynamics 429D.7 Electroweak interactions 434D.7.1 Weak isospin 434D.7.2 Gauge invariance and charged currents 436D.7.3 The unification condition 437D.7.4 Spin structure and parity violation 440Problems D 441E Answers to selected questions 443References 448Index 451