Elementary Particle Physics Lecture Notes 2009 (December 13, 2013) Paolo Franzini University of Rome, La Sapienza http://www.lnf.infn.it/~paolo/ pp09 ii pf-pp This notes are \my notes", to remind myself of what I want to talk about, they are not a text book! The notes are quite incomplete. While almost all that appears in the notes has been presented in class, many topics presented are missing. p The factor i = −1 and the sign for amplitudes is almost always ignored in the notes, an exception being when exchanging fermions and/or bosons. Likewise µ factors eik xµ which are supposed to be there are omitted almost always. There are some repetitions due to merging of files. That will be fixed, some- times, maybe. Contents 1 Introduction 1 1.1 History ................................ 1 1.2 Elementary particles ........................ 1 1.3 Masses ................................ 4 1.4 Conserved additive quantities ................... 5 1.5 Natural Units: ~=c=1 ....................... 6 1.6 The Electromagnetic Interaction .................. 8 1.6.1 The many meanings of α .................. 9 1.7 The Gravitational Interaction ................... 10 1.8 Interactions and coupling constants ................ 11 2 Order of Magnitude Calculations 15 2.1 Introduction ............................. 15 2.2 e+e−!µ+µ− ............................. 15 2.3 ν + N!::: ............................. 17 2.4 Compton scattering ......................... 17 2.5 Muon decay ............................. 18 2.6 Pair production and bremsstrahlung ............... 19 2.7 High energy hadronic total cross sections ............. 21 3 Reaction Rates and Cross Section 23 3.1 S-matrix, T and transition probability. .............. 23 3.2 Decay rate, three bodies ...................... 24 3.2.1 Integration Limits ...................... 26 3.2.2 Normalized variables .................... 28 3.3 Decay rate, two bodies ....................... 29 3.4 Scattering cross section ....................... 30 3.5 Accounting for Spin ......................... 32 3.5.1 Traces ............................ 33 3.5.2 Vector current ........................ 34 3.5.3 V-A coupling ........................ 34 iv pf-pp CONTENTS 4 The Electromagnetic Interaction 35 4.1 Introduction: Classical Rutherford Scattering .......... 35 4.1.1 Exact computation of ∆p ................. 36 4.1.2 Final remarks ........................ 37 4.2 The Elementary EM Interaction .................. 37 4.3 The Rutherford cross section .................... 39 4.4 EM Scattering of Spinless Particles ................ 41 4.5 Pion Compton Scattering ..................... 43 4.6 Extended Charge Distribution, I .................. 46 4.7 Extended Charge Distribution, II ................. 47 4.8 Scattering with Spin ........................ 50 4.9 e+e− ! π+π− ............................ 54 4.10 e+e− ! µ+µ− ............................ 56 4.11 Summary .............................. 58 5 The Weak Interaction. I 59 5.1 Introduction ............................. 59 5.2 Parity and Charge Conjugation .................. 61 5.3 Helicity and left-handed particles ................. 63 5.4 The V−A interaction ........................ 64 5.5 Muon Decay ............................. 65 5.6 Semileptonic weak decays ..................... 69 5.7 Quarks and the weak current ................... 69 5.8 Pion Decay ............................. 71 5.8.1 Pion decay to lepton plus neutrino ............ 71 5.8.2 π± decay to π0, electron and neutrino ........... 73 5.9 Inverse muon decay. ......................... 73 6 Strangeness 75 6.1 K mesons .............................. 75 6.2 The Strange Problem ........................ 76 6.2.1 Strangeness Selection Rules ................ 77 6.2.2 Charge and I3 ........................ 78 6.3 Kaons and Parity Violation .................... 80 6.4 Strangeness Changing Weak Interaction .............. 81 6.5 Hyperons .............................. 81 6.5.1 Measuring the spin of the Λ0 ................ 82 6.5.2 Σ decays ........................... 84 6.5.3 Computing the amplitudes ................. 84 6.6 Non Leptonic Kaon Decays .................... 86 6.6.1 Outgoing Waves ....................... 86 6.6.2 K ! 2π decays ....................... 87 6.7 Semileptonic Kaon Decays ..................... 89 CONTENTS pf-pp v 6.8 Cabibbo Mixing ........................... 90 6.9 Kaon Mass and CP eigenstates .................. 90 6.10 K1 and K2 lifetimes and mass difference ............. 91 6.11 Strangeness oscillations ....................... 92 6.12 Regeneration ............................ 94 7 The Weak Interaction II. CP 97 7.1 CP Violation in Two Pion Decays ................. 97 7.1.1 The super-weak possibility ................. 99 7.1.2 Direct CP violation ..................... 100 7.2 CP Violation at a ϕ{factory .................... 102 7.2.1 ϕ (Υ000) production and decay in e+e− annihilations ... 102 7.2.2 Correlations in KS, KL decays ............... 103 7.3 CP Violation in Other Modes ................... 106 7.3.1 Semileptonic decays ..................... 106 7.4 CP violation in KS decays ..................... 107 7.5 CP violation in charged K decays ................. 108 7.6 Neutral Kaon Properties ...................... 109 7.6.1 CPLEAR .......................... 109 7.6.2 ∆m and ϕ+− ........................ 109 7.7 CPT Invariance ........................... 110 7.8 CP Violation Experiments ..................... 110 8 Quark Mixing 113 8.1 GIM and the c-quark ........................ 113 8.1.1 The KL-KS mass difference and the c-quark mass .... 114 8.1.2 6 quarks ........................... 115 8.1.3 Counting parameters .................... 117 8.1.4 Determination of the CKM parameter Vus ........ 118 8.2 Testing Unitarity .......................... 120 8.2.1 Wolfenstein parametrization ................ 120 8.2.2 Unitary triangles ...................... 121 8.3 Rare K Decays ........................... 123 8.3.1 Search for K+!π+νν¯ ................... 124 0 8.3.2 KL!π νν¯ .......................... 124 9 B decays and CP 127 9.1 B semileptonic decays ....................... 127 9.2 BB¯ Mixing ............................. 128 9.2.1 DISCOVERY ........................ 128 9.3 CP Violation ............................ 131 9.4 CDF and DØ ............................ 133 9.5 B-factories .............................. 133 vi pf-pp CONTENTS 9.6 LHC ................................. 134 9.7 CP , kaons and B-mesons: the future ............... 134 10 The Weak Interaction. III 137 10.1 Beauty Decays ........................... 137 10.2 Charm Decays ............................ 139 10.3 Decay Rate ............................. 140 10.4 Other Things ............................ 140 10.5 Contracting two indexes. ...................... 140 10.6 Triple Product \Equivalent". .................... 141 11 Quantum Chromo Dynamics 143 11.1 e+e−!Hadrons ........................... 143 11.2 Quark model ............................ 143 11.2.1 qq¯ .............................. 143 11.2.2 qqq .............................. 144 11.3 GAUGE INVARIANCE ...................... 145 11.3.1 QED ............................. 145 11.3.2 Quantum Chromodynamics ................ 148 12 Hadron Spectroscopy 155 13 High Energy Scattering 161 14 The Electro-weak Interaction 163 15 Spontaneous Symmetry Breaking, the Higgs Scalar 165 15.1 Introduction ............................. 165 16 Neutrino Oscillation 167 16.1 Introduction ............................. 167 16.2 Two neutrinos oscillation ...................... 168 17 Neutrino Experiments. A Seminar 171 17.1 The invention of the neutrino ................... 171 17.2 Neutrino Discovery ......................... 171 17.3 Something different, neutrinos from the sun ........... 173 17.4 Reactor and high energy ν's .................... 186 17.5 The missing ν's are found ..................... 190 17.6 Future Experiments ......................... 194 18 The Muon Anomaly. A Seminar 197 18.1 Introduction ............................. 197 18.2 g for Dirac particles ......................... 198 18.3 Motion and precession in a B field ................. 198 CONTENTS pf-pp vii 18.4 The first muon g − 2 experiment .................. 200 18.5 The BNL g-2 experiment ...................... 201 18.6 Computing a = g=2 − 1 ....................... 206 18.7 aµ .................................. 206 18.8 HADRONS ............................. 207 18.9 σ(e+e− ! π+π−) .......................... 208 19 Higgs Bosons Today. A Seminar 213 19.1 Why are Higgs so popular? ..................... 213 19.2 Weak Interaction and Intermediate Boson ............ 215 19.3 Searching for Higgs. Where? .................... 217 19.4 Searching fo Higgs. How? ..................... 221 Appendices 233 A Kinematics 233 A.1 4-vectors ............................... 233 A.2 Invariant Mass ........................... 234 A.3 Other Concepts ........................... 234 A.4 Trasformazione di uno spettro di impulsi ............. 236 A.5 Esempi ................................ 239 A.5.1 Decadimenti a due corpi .................. 239 A.5.2 Decadimenti a tre corpi .................. 240 A.5.3 Decadimento π ! µν .................... 240 A.5.4 Annichilazioni e+-e− .................... 241 A.5.5 Angolo minimo tra due fotoni da π0 ! γγ ........ 242 A.5.6 Energia dei prodotti di decadimenti a tre corpi ...... 242 A.5.7 2 particelle!2 particelle .................. 242 A.6 Limite di massa infinita e limite non relativistico ......... 243 A.6.1 Esercizio ........................... 245 B L − J − S, SU(2,3), g; a 247 B.1 Orbital angular momentum ...................