FYS3510 Subatomic Physics VS 2015 Farid Ould-Saada Exam 2016 In addition to the items marked in blue, don t forget all examples and related material given in the slides, including the ones presented during the CERN visit, as well as the problems proposed. This year, more emphasis will be given to basic concepts, both theoretical (conservation laws, symmetries, quantum numbers, basic interactions, (relativistic) kinematics, transition probabilities, Feynman diagrams, nuclear models, decays, to name only a few) and experimental (particle detection and detectors, particle interactions with matter, main discoveries, to name only a few). The examples from 2015 and previous years can be accessed through the webpage of the course: http://folk.uio.no/farido/fys3510-16.html, see also links to the previous years. Particles and Fundamental interactions, 2012, Braibant et al. Additional material covering introduction to heavy ion physics Exam pensum In addition to the parts of the book highlighted in blue, the material shown in the class (and included in the slides made available), the lectures given at CERN (in particular the introduction on heavy ion collisions), and all examples and exercises treated / suggested (in the accompanying book, in the assignments, and in the lectures/slides) are very relevant for the exam. 1 Historical Notes and Fundamental Concepts 1 1.1 Introduction 1 1.2 The Discovery of Particles 3 1.3 The Concept of the Atom and Indivisibility 5 1.4 The Standard Model of Microcosm Fundamental Fermions and Bosons 9 2 Particle Interactions with Matter and Detectors 11 Emphasis in this chapter is on concepts and principles: how do various particles loose energy in matter? How are particles detected? 2.1 Introduction 11 2.2 Passage of Charged Particles Through Matter 12 2.2.1 Energy Loss Through Ionization and Excitation 12 2.2.2 Classical Calculation of Energy Loss Through Ionization 13 2.2.3 Bremsstrahlung 20 2.3 Photon Interactions 22 2.3.1 Photoelectric Effect 22 2.3.2 Compton Scattering 23 2.3.3 Pair Production 25 2.4 Electromagnetic Showers 25 2.5 Neutron Interactions 28
2.6 Qualitative Meaning of a Total Cross-Section Measurement 29 2.7 Techniques of Particle Detection 30 2.7.1 General Characteristics 30 2.8 Ionization Detectors 32 2.9 Scintillation Counters 35 2.10 Semiconductor Detectors 38 2.11 Cherenkov Counters 39 2.12 The Bubble Chamber 40 2.13 Electromagnetic and Hadronic Calorimeters 42 3 Particle Accelerators and Particle Detection 45 Emphasis in the accelerators part this chapter is on concepts and principles: how are charged particles accelerated and collided? Collider vs fixed target mode. Very important are (i) the way some key particle properties are measured and (ii) the detailed use of (relativistic) kinematics as well as basics of quantum mechanics. Centre of mass vs laboratory frame. Relativistic invariants. To be studied together with Appendices A.2, A.3. 3.1 Why Do We Need Accelerators? 45 3.1.1 The Center-of-Mass (c.m.) System 47 3.1.2 The Laboratory System 47 3.1.3 Fixed Target Accelerator and Collider 48 3.2 Linear and Circular Accelerators 49 3.2.1 Linear Accelerators 49 3.2.2 Circular Accelerators 50 3.3 Colliders and Luminosity 52 3.3.1 Example: the CERN Accelerator Complex 53 3.4 Conversion of Energy into Mass 54 3.4.1 Use of Fixed Target Accelerators 55 3.4.2 Baryonic Number Conservation 57 3.5 Particle Production in a Secondary Beam 57 3.5.1 Time-of-Flight Spectrometer 57 3.6 Bubble Chambers in Charged Particle Beams 61 3.6.1 Conservation Laws 61 3.6.2 The Electron Spiral 64 3.6.3 Electron-Positron Pair 65 3.6.4 An Electron-Positron Tree 66 3.6.5 Charged Particle Decays 67 4 The Paradigm of Interactions: The Electromagnetic Case 73 4.1 The Interaction Between Electric Charges 74 4.1.1 The EM Coupling Constant 76 4.1.2 The Quantum Theory of Electromagnetism 78 4.2 Some Quantum Mechanics Concepts 78 4.2.1 The Schrödinger Equation 79 4.2.2 Klein Gordon Equation 80 4.2.3 Dirac Equation 81 4.3 Transition Probabilities in Perturbation Theory 82 4.4 The Bosonic Propagator 85 4.5 Cross-Sections and Lifetime: Theory and Experiment 86 4.5.1 The Cross-Section 86 4.5.2 Particle Decay and Lifetime 88 4.6 Feynman Diagrams 90 4.7 A Few Examples of Electromagnetic Processes 93
4.7.1 Rutherford Scattering 93 4.7.2 The e+e-àµ+ µ - Process 97 4.7.3 Elastic Scattering e+e-àe+e- (Bhabha Scattering) 98 4.7.4 e+e-àγγannihilation 99 4.7.5 Some QED Checks 99 5 First Discussion of the Other Fundamental Interactions 101 5.1 Introduction 101 5.2 The Gravitational Interaction 101 5.3 The Weak Interaction 103 5.4 The Strong Interaction 106 5.5 Particle Classification 109 5.5.1 Classification According to Stability 110 5.5.2 Classification According to the Spin 110 5.5.3 Classification According to the Baryon and Lepton Numbers 111 6 Invariance and Conservation Principles 113 6.1 Introduction 113 6.2 Invariance Principle Reminder 114 6.2.1 Invariance in Classical Mechanics 114 6.2.2 Invariance in Quantum Mechanics 115 6.2.3 Continuous Transformations: Translations and Rotations 117 6.3 Spin-Statistics Connection 118 6.4 Parity 119 6.5 Spin-Parity of the π Meson 122 6.5.1 Spin of the π Meson 122 6.5.2 Parity of the π Meson 123 6.5.3 Particle Antiparticle Parity 125 6.6 Charge Conjugation 126 6.6.1 Charge Conjugation in Electromagnetic Processes 127 6.6.2 Violation of C in the Weak Interaction 128 6.7 Time Reversal 129 6.8 CP and CPT 131 6.9 Electric Charge and Gauge Invariance 133 7 Hadron Interactions at Low Energies and the Static Quark Model 135 7.1 Hadrons and Quarks 135 7.1.1 The Yukawa Model 136 7.2 Proton-Neutron Symmetry and the Isotopic Spin 137 7.3 The Strong Interaction Cross-Section 139 7.3.1 Mean Free Path 140 7.4 Low Energy Hadron-Hadron Collisions 142 7.4.1 Antibaryons 143 7.4.2 Hadron Resonances 144 7.5 Breit Wigner Equation for Resonances 148 7.5.1 The _CC.1232/ Resonance 150 7.5.2 Resonance Formation and Production 151 7.5.3 Angular Distribution of Resonance Decay Products 152 7.6 Production and Decay of Strange Particles 154 7.7 Classification of Hadrons Made of u; d; s Quarks 156 7.8 The JP = 3/2C Baryonic Decuplet 158 7.8.1 First Indications for the Color Quantum Number 160 7.9 The JP =1/2C Baryonic Octet 162
7.10 Pseudoscalar Mesons 163 7.11 The Vector Mesons 165 7.12 Strangeness and Isospin Conservation 167 7.13 The Six Quarks 168 7.14 Experimental Tests on the Static Quark Model 170 7.14.1 Leptonic Decays of Neutral Vector Mesons 170 7.14.2 Lepton Pair Production 171 7.14.3 Hadron-Hadron Cross-Sections at High Energies 172 7.14.4 Baryon Magnetic Moments 173 7.14.5 Relations Between Masses 175 7.15 Searches for Free Quarks and Limits of the Model 177 8 Weak Interactions and Neutrinos 179 8.1 Introduction 179 8.2 The Neutrino Hypothesis and the β Decay 180 8.2.1 Nuclear β Decay and the Missing Energy 180 8.2.2 The Pauli Desperate Remedy 181 8.2.3 How World War II Accelerated the Neutrino Discovery 183 8.3 Fermi Theory of Beta Decay 184 8.3.1 Neutron Decay 185 8.3.2 The Fermi Coupling Constant from Neutron β Decay 186 8.3.3 The Coupling Constant W from Fermi Theory 187 8.4 Universality of Weak Interactions (I) 187 8.4.1 Muon Lifetime 187 8.4.2 The Sargent Rule 189 8.4.3 The Puppi Triangle 189 8.5 The Discovery of the Neutrino 190 8.5.1 The Poltergeist Project 190 8.6 Different Transition Types in β Decay 194 8.6.1 The Cross-Section of the β-inverse Process 197 8.7 Lepton Families 198 8.8 Parity Violation in β Decays 201 8.9 The Two-Component Neutrino Theory 204 8.10 Charged Pion Decay 205 8.11 Strange Particle Decays 208 8.12 Universality of Weak Interactions (II). The Cabibbo Angle 211 8.13 Weak Interaction Neutral Current 213 8.14 Weak Interactions and Quark Eigenstates 215 8.14.1 The WI Hamiltonian and the GIM Mechanism 215 8.14.2 Hints on the Fourth Quark fromwi Neutral Currents 217 8.14.3 The Six Quarks and the Cabibbo Kobayashi MaskawaMatrix 218 8.15 Discovery of the W and Z0 Vector Bosons 220 8.16 The V-A Theory of CC Weak Interaction 222 Features of weak interactions (implementation of parity violation through V-A) and difference with the electromagnetic interaction are important and must be understood (discussed/summarised in the lectures). 8.16.1 Bilinear Forms of Dirac Fermions 222 8.16.2 Current CurrentWeak Interaction 225 9 Discoveries in Electron-Positron Collisions 229 9.1 Introduction 229 9.2 e+-e- Cross-Section and the Determination of the Number of Colors 231
9.2.1 The Process e+e-àγàµ+µ- 232 9.2.2 The Color Quantum Number 232 9.3 The Discovery of Charm and Beauty Quarks 234 9.3.1 Mesons with c, c Quarks 234 9.3.2 The J= Resonance Properties 235 9.3.3 Mesons with b, b Quarks 236 9.4 Spectroscopy of Heavy Mesons and α S Estimate 237 9.5 The τ Lepton 238 9.6 LEP Experiments and Examples of Events at LEP 239 9.6.1 The LEP Detectors 239 9.6.2 Events in 4π Detectors at LEP 243 9.7 e+e- Collisions at E cm ~91GeV. The Z0 Boson 248 9.7.1 The Z0 Resonance 248 9.7.2 Z0 Total and Partial Widths 249 9.7.3 Measurable Quantities, Γ invis & Nber of Light Neutrino Families 251 9.7.4 Forward Backward Asymmetries A FB 253 9.7.5 Multihadronic Production Model 256 9.8 e+e- Collisions for sqrt(s) > 100 GeV at LEP2 257 9.8.1 e+e-àw+w-, Z0Z0 Cross-Sections 258 9.8.2 The W Boson Mass and Width 261 9.8.3 Measurement of α S 262 9.8.4 The Higgs Boson Search at LEP 262 10 High Energy Interactions and the Dynamic Quark Model 265 10.1 Introduction 265 10.2 Lepton Nucleon Interactions at High Energies 265 10.3 Elastic Electron-Proton Scattering 269 10.3.1 Kinematic Variables 269 10.3.2 Proton Form Factors 270 10.4 Inelastic ep Cross-Section 275 10.4.1 Partons in the Nucleons: Their Nature and Spin 278 10.4.2 Electric Charge of the Partons 280 10.5 Cross-Section for CC N Interactions 282 10.5.1 Comparison with Experimental Data 287 10.5.2 The Neutrino-Nucleon Cross-Section 288 10.6 Naive and Advanced Quark Models 290 10.6.1 Q2-Dependence of the Structure Functions 290 10.6.2 Summary of DIS Results 294 10.7 High Energy Hadron-Hadron Collisions 296 10.8 Total and Elastic Cross-Sections at High Energy 298 10.8.1 Elastic Differential Cross-Sections 298 10.8.2 Total Cross-Sections 301 10.9 High Energy Inelastic Hadron Collisions at Low-pt 302 10.9.1 Outline on High Energy Nucleus-Nucleus Collisions 303 10.10 The LHC and the Search for the Higgs Boson 305 10.10.1 Higgs Boson Production in pp Collisions 306 10.10.2 Higgs Boson Decays 308 10.10.3 Search Strategies at LHC 309 11 The Standard Model of the Microcosm 313 We already discussed several aspects of the SM of electroweak and strong interactions. Not time to go through the full formalism of gauge theories (will be done in FYS4170 and FYS4560
thoroughly). The Higgs in discussed in the lectures (chapter 9), including the slides presented at CERN on ATLAS, Higgs and other searches, as well as the slides shown in the lectures. In particular it is important to know how the Higgs is produced in e+e- and hadron colliders, how it decays depending of its mass and how it is discovered! Other items of this chapter already cover in previous chapter (slides and partly book): QED and QCD (running coupling constants, asymptotic freedom, charge screening, color (factors); parameters of the SM. 11.1 Introduction 313 11.2 Weak Interaction Divergences and Unitarity Problem 314 11.3 Gauge Theories 316 11.3.1 Choice of the Symmetry Group 317 11.3.2 Gauge Invariance 318 11.4 Gauge Invariance in the Electroweak Interaction 322 11.4.1 Lagrangian Density of the Electroweak Theory 323 11.5 Spontaneous Symmetry Breaking. The Higgs Mechanism 325 11.6 The Weak Neutral Current 330 11.7 The Fermion Masses 333 11.8 Parameters of the Electroweak Interaction 334 11.8.1 Electric Charge Screening in QED 336 11.8.2 HO Feynman Diagrams, Mathematical Infinities and Renormalization in QED 337 11.9 The Strong Interaction 338 11.9.1 Quantum Chromodynamics (QCD) 338 11.9.2 Color Charge Screening in QCD 341 11.9.3 Color Factors 342 11.9.4 The Strong Coupling Constant α S 343 11.10 The Standard Model: A Summary 343 12 CP-Violation and Particle Oscillations 347 We already discussed some of the aspects of the K0-K0bar system in chapter 8 and introduced the CKM matrix and the introduction of a phase to incorporate CP violation in the SM. We briefly discussed strangeness violation and K0-K0bar (and the corresponding oscillations in the neutral D- and B-systems). Time does not allow us to go through the formalism of oscillations and CP violation, unfortunately. 12.1 The Matter-Antimatter Asymmetry Problem 347 12.2 The K0K0bar System 348 12.2.1 Time Development of a K0 Beam. K01 Regeneration. Strangeness Oscillations 350 12.3 CP-Violation in the K0-K0bar System 353 12.3.1 The Formalism and the Parameters of CP-Violation 354 12.4 What is the Reason for CP-Violation? 358 12.5 CP-Violation in the B0-B0bar System 360 12.5.1 Future Experiments 364 12.6 Neutrino Oscillations 364 12.6.1 The Special Case of Oscillations Between Two Flavors 365 12.6.2 Three Flavor Oscillations 367 12.6.3 The Approximation for a Neutrino with Dominant Mass 368 12.6.4 Neutrino Oscillations in Matter 370 12.7 Neutrinos from the Sun and Oscillation Studies 371 12.8 Atmospheric Oscillations and Experiments 376 12.8.1 Long Baseline Experiments 379 12.9 Effects of Neutrino Oscillations 381
13 Microcosm and Macrocosm 385 Lectures given at CERN on new physics can be found here: 2016 and 2015 13.1 The Grand Unification 386 13.1.1 Proton Decay 389 13.1.2 Magnetic Monopoles 390 13.1.3 Cosmology. First Moment of the Universe 391 13.2 Supersymmetry (SUSY) 392 13.2.1 Minimal Standard Supersymmetric Model (MSSM) 393 13.2.2 Supergravity (SUGRA). Superstrings 397 13.3 Composite Models 397 13.4 Particles, Astrophysics and Cosmology 400 13.5 Dark Matter 403 13.6 The Big Bang and the Primordial Universe 407 14 Fundamental Aspects of Nucleon Interactions 415 This chapter on nuclear physics is too thin in the book. It must be studied together with the lecture material. The slides treat several important examples that will be part of the exam. Several nuclear physics related subjects are scattered through the other chapters (4,7 and 10, especially). Heavy ions collisions are treated in the CERN lecture. Emphasis is there on the concepts, measurements and interpretation of results (quark gluon plasma, collective behaviors, ). 14.1 Introduction 415 14.2 General Properties of Nuclei 417 14.2.1 The Chart of Nuclides 419 14.2.2 Nuclear Binding Energy 420 14.2.3 Size of the Nuclei 421 14.2.4 Electromagnetic Properties of the Nuclei 424 14.3 Nuclear Models 424 14.3.1 Fermi Gas Model 425 14.3.2 Nuclear Drop Model 426 14.3.3 Shell Model 429 14.4 Properties of Nucleon-Nucleon Interaction 431 14.5 Radioactive Decay and Dating 433 14.5.1 Cascade Decays 434 14.6 γ Decay 436 14.7 α Decay 437 14.7.1 Elementary Theory of α Decay 439 14.7.2 Lifetime Calculation of the 238 92U Nucleus 440 1 4.8 β Decay 441 14.8.1 Elementary Theory of Nuclear β-decay 443 14.9 Nuclear Reactions and Nuclear Fission 444 14.9.1 Nuclear Fission 445 14.9.2 Fission Nuclear Reactors 447 14.10 Nuclear Fusion in Astrophysical Environments 448 14.10.1 Fusion in Stars 449 14.10.2 Formation of Elements Heavier than Fe in Massive Stars 451 14.10.3 Earth and Solar System Dating 454 14.11 Nuclear Fusion in Laboratory 455 15 Heavy ion collisions at the LHC
15.1 See Heavy ion lecture (2015) and High-energy nuclear physics at the LHC (2016) during the CERN visit 15.2 See Slides (HE heavy ion physics) from previous years, complementing the CERN lecture Appendix A 459 Appendices A.2, A.3 and A.4 are complemented with additional, important information in the lectures, slides and exercises! To be studied all together! A.1 Periodic Table [P08] 460 A.2 The Natural Units in Sub-nuclear Physics 461 A.3 Basic Concepts of Relativity and Classical Electromagnetism 462 A.3.1 The Formalism of Special Relativity 462 A.3.2 The Formalism of Classical Electromagnetism 464 A.3.3 Gauge Invariance of the Electromagnetism 466 A.4 Dirac Equation and Formalism 467 Emphasis is on what was presented in the lectures (slides) / exercises. A.4.1 Derivation of the Dirac Equation 467 A.4.2 General Properties of the Dirac Equation 469 A.4.3 Properties of the Dirac Equation Solutions 472 A.4.4 Helicity Operator and States 475 Important is here the concept of helicity of relativistic particles and its relation to the mass of particles (p.477). These concepts were used in discussion weak interactions. A.5 Physical and Astrophysical Constants [P08] 478 References 481 Index 487