FYS3510 – Subatomic Physics VS 2015
Farid Ould-Saada
Exam 2015 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 2014 and previous years can be accessed through the webpage of the course:
http://folk.uio.no/farido/fys3510-15.html, see also links to the previous years.
Exam pensum 1 Historical Notes and Fundamental Concepts
1.1 Introduction
1.2 The Discovery of Particles
1.3 The Concept of the Atom and Indivisibility
1.4 The Standard Model of Microcosm – Fundamental Fermions and Bosons
2 Particle Interactions with Matter and Detectors
2.1 Introduction
2.2 Passage of Charged Particles Through Matter
2.2.1 Energy Loss Through Ionization and Excitation
2.2.2 “Classical” Calculation of Energy Loss Through Ionization
2.2.3 Bremsstrahlung
2.3 Photon Interactions
2.3.1 Photoelectric Effect
2.3.2 Compton Scattering
2.3.3 Pair Production
2.4 Electromagnetic Showers
2.5 Neutron Interactions
2.6 Qualitative Meaning of a Total Cross-Section Measurement
2.7 Techniques of Particle Detection
2.7.1 General Characteristics
2.8 Ionization Detectors
2.9 Scintillation Counters
2.10 Semiconductor Detectors
2.11 Cherenkov Counters
2.12 The Bubble Chamber
2.13 Electromagnetic and Hadronic Calorimeters
3 Particle Accelerators and Particle Detection
3.1 Why Do We Need Accelerators?
3.1.1 The Center-of-Mass (c.m.) System
1
1
3
5
9
11
11
12
12
13
20
22
22
23
25
25
28
29
30
30
32
35
38
39
40
42
45
45
47
3.1.2 The Laboratory System
3.1.3 Fixed Target Accelerator and Collider
3.2 Linear and Circular Accelerators
3.2.1 Linear Accelerators
3.2.2 Circular Accelerators
3.3 Colliders and Luminosity
3.3.1 Example: the CERN Accelerator Complex
3.4 Conversion of Energy into Mass
3.4.1 Use of Fixed Target Accelerators
3.4.2 Baryonic Number Conservation
3.5 Particle Production in a Secondary Beam
3.5.1 Time-of-Flight Spectrometer
3.6 Bubble Chambers in Charged Particle Beams
3.6.1 Conservation Laws
3.6.2 The Electron “Spiral”
3.6.3 Electron-Positron Pair
3.6.4 An Electron-Positron “Tree”
3.6.5 Charged Particle Decays
4 The Paradigm of Interactions: The Electromagnetic Case
4.1 The Interaction Between Electric Charges
4.1.1 The EM Coupling Constant
4.1.2 The Quantum Theory of Electromagnetism
4.2 Some Quantum Mechanics Concepts
4.2.1 The Schr¨odinger Equation
4.2.2 Klein–Gordon Equation
4.2.3 Dirac Equation
4.3 Transition Probabilities in Perturbation Theory
4.4 The Bosonic Propagator
4.5 Cross-Sections and Lifetime: Theory and Experiment
4.5.1 The Cross-Section
4.5.2 Particle Decay and Lifetime
4.6 Feynman Diagrams
4.7 A Few Examples of Electromagnetic Processes
4.7.1 Rutherford Scattering
4.7.2 The e+e-àµ+ µ - Process
4.7.3 Elastic Scattering e+e-àe+e- (Bhabha Scattering)
4.7.4 e+e-àγγAnnihilation
4.7.5 Some QED Checks
5 First Discussion of the Other Fundamental Interactions
5.1 Introduction
5.2 The Gravitational Interaction
5.3 The Weak Interaction
5.4 The Strong Interaction
5.5 Particle Classification
5.5.1 Classification According to Stability
5.5.2 Classification According to the Spin
5.5.3 Classification According to the Baryon and Lepton Numbers
6 Invariance and Conservation Principles
6.1 Introduction
6.2 Invariance Principle Reminder
6.2.1 Invariance in Classical Mechanics
6.2.2 Invariance in Quantum Mechanics
47
48
49
49
50
52
53
54
55
57
57
57
61
61
64
65
66
67
73
74
76
78
78
79
80
81
82
85
86
86
88
90
93
93
97
98
99
99
101
101
101
103
106
109
110
110
111
113
113
114
114
115
6.2.3 Continuous Transformations: Translations and Rotations
6.3 Spin-Statistics Connection
6.4 Parity
6.5 Spin-Parity of the π Meson
6.5.1 Spin of the π Meson
6.5.2 Parity of the π Meson
6.5.3 Particle–Antiparticle Parity
6.6 Charge Conjugation
6.6.1 Charge Conjugation in Electromagnetic Processes
6.6.2 Violation of C in the Weak Interaction
6.7 Time Reversal
6.8 CP and CPT
6.9 Electric Charge and Gauge Invariance
7 Hadron Interactions at Low Energies and the Static Quark Model
7.1 Hadrons and Quarks
7.1.1 The Yukawa Model
7.2 Proton-Neutron Symmetry and the Isotopic Spin
7.3 The Strong Interaction Cross-Section
7.3.1 Mean Free Path
7.4 Low Energy Hadron-Hadron Collisions
7.4.1 Antibaryons
7.4.2 Hadron Resonances
7.5 Breit–Wigner Equation for Resonances
7.5.1 The _CC.1232/ Resonance
7.5.2 Resonance Formation and Production
7.5.3 Angular Distribution of Resonance Decay Products
7.6 Production and Decay of Strange Particles
7.7 Classification of Hadrons Made of u; d; s Quarks
7.8 The JP = 3/2C Baryonic Decuplet
7.8.1 First Indications for the Color Quantum Number
7.9 The JP =1/2C Baryonic Octet
7.10 Pseudoscalar Mesons
7.11 The Vector Mesons
7.12 Strangeness and Isospin Conservation
7.13 The Six Quarks
7.14 Experimental Tests on the Static Quark Model
7.14.1 Leptonic Decays of Neutral Vector Mesons
7.14.2 Lepton Pair Production
7.14.3 Hadron-Hadron Cross-Sections at High Energies
7.14.4 Baryon Magnetic Moments
7.14.5 Relations Between Masses
7.15 Searches for Free Quarks and Limits of the Model
8 Weak Interactions and Neutrinos
8.1 Introduction
8.2 The Neutrino Hypothesis and the β Decay
8.2.1 Nuclear β Decay and the Missing Energy
8.2.2 The Pauli Desperate Remedy
8.2.3 How World War II Accelerated the Neutrino Discovery
8.3 Fermi Theory of Beta Decay
8.3.1 Neutron Decay
8.3.2 The Fermi Coupling Constant from Neutron β Decay
8.3.3 The Coupling Constant ˛W from Fermi Theory
117
118
119
122
122
123
125
126
127
128
129
131
133
135
135
136
137
139
140
142
143
144
148
150
151
152
154
156
158
160
162
163
165
167
168
170
170
171
172
173
175
177
179
179
180
180
181
183
184
185
186
187
8.4 Universality of Weak Interactions (I)
8.4.1 Muon Lifetime
8.4.2 The Sargent Rule
8.4.3 The Puppi Triangle
8.5 The Discovery of the Neutrino
8.5.1 The Poltergeist Project
8.6 Different Transition Types in β Decay
8.6.1 The Cross-Section of the β-Inverse Process
8.7 Lepton Families
8.8 Parity Violation in β Decays
8.9 The Two-Component Neutrino Theory
8.10 Charged Pion Decay
8.11 Strange Particle Decays
8.12 Universality of Weak Interactions (II). The Cabibbo Angle
8.13 Weak Interaction Neutral Current
8.14 Weak Interactions and Quark Eigenstates
8.14.1 The WI Hamiltonian and the GIM Mechanism
8.14.2 Hints on the Fourth Quark fromWI Neutral Currents
8.14.3 The Six Quarks and the Cabibbo–Kobayashi–MaskawaMatrix
8.15 Discovery of the W˙ and Z0 Vector Bosons
8.16 The V-A Theory of CC Weak Interaction
8.16.1 Bilinear Forms of Dirac Fermions
8.16.2 Current–CurrentWeak Interaction
9 Discoveries in Electron-Positron Collisions
9.1 Introduction
9.2 e+-e- Cross-Section and the Determination of the Number of Colors
9.2.1 The Process e+e-àγàµ+µ9.2.2 The Color Quantum Number
9.3 The Discovery of Charm and Beauty Quarks
9.3.1 Mesons with c, c Quarks
9.3.2 The J= Resonance Properties
9.3.3 Mesons with b, b Quarks
9.4 Spectroscopy of Heavy Mesons and αS Estimate
9.5 The τ Lepton
9.6 LEP Experiments and Examples of Events at LEP
9.6.1 The LEP Detectors
9.6.2 Events in 4π Detectors at LEP
9.7 e+e- Collisions at Ecm ~91GeV. The Z0 Boson
9.7.1 The Z0 Resonance
9.7.2 Z0 Total and Partial Widths
9.7.3 Measurable Quantities, Γinvis & Nber of Light Neutrino Families
9.7.4 Forward–Backward Asymmetries AFB
9.7.5 Multihadronic Production Model
9.8 e+e- Collisions for sqrt(s) > 100 GeV at LEP2
9.8.1 e+e-àW+W-, Z0Z0 Cross-Sections
9.8.2 The W Boson Mass and Width
9.8.3 Measurement of αS
9.8.4 The Higgs Boson Search at LEP
10 High Energy Interactions and the Dynamic Quark Model
10.1 Introduction
10.2 Lepton–Nucleon Interactions at High Energies
10.3 Elastic Electron-Proton Scattering
187
187
189
189
190
190
194
197
198
201
204
205
208
211
213
215
215
217
218
220
222
222
225
229
229
231
232
232
234
234
235
236
237
238
239
239
243
248
248
249
251
253
256
257
258
261
262
262
265
265
265
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
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 αS
343
11.10 The Standard Model: A Summary
343
12 CP-Violation and Particle Oscillations
347
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
12.6.2 Three Flavor Oscillations
12.6.3 The Approximation for a Neutrino with Dominant Mass
12.6.4 Neutrino Oscillations in Matter
12.7 Neutrinos from the Sun and Oscillation Studies
12.8 Atmospheric __ Oscillations and Experiments
12.8.1 Long Baseline Experiments
12.9 Effects of Neutrino Oscillations
13 Microcosm and Macrocosm
13.1 The Grand Unification
13.1.1 Proton Decay
13.1.2 Magnetic Monopoles
13.1.3 Cosmology. First Moment of the Universe
13.2 Supersymmetry (SUSY)
13.2.1 Minimal Standard Supersymmetric Model (MSSM)
13.2.2 Supergravity (SUGRA). Superstrings
13.3 Composite Models
13.4 Particles, Astrophysics and Cosmology
13.5 Dark Matter
13.6 The Big Bang and the Primordial Universe
14 Fundamental Aspects of Nucleon Interactions
14.1 Introduction
14.2 General Properties of Nuclei
14.2.1 The Chart of Nuclides
14.2.2 Nuclear Binding Energy
14.2.3 Size of the Nuclei
14.2.4 Electromagnetic Properties of the Nuclei
14.3 Nuclear Models
14.3.1 Fermi Gas Model
14.3.2 Nuclear Drop Model
14.3.3 Shell Model
14.4 Properties of Nucleon-Nucleon Interaction
14.5 Radioactive Decay and Dating
14.5.1 Cascade Decays
14.6 γ Decay
14.7 α Decay
14.7.1 Elementary Theory of α Decay
14.7.2 Lifetime Calculation of the 238 92U Nucleus
1
4.8 β Decay
14.8.1 Elementary Theory of Nuclear β-Decay
14.9 Nuclear Reactions and Nuclear Fission
14.9.1 Nuclear Fission
14.9.2 Fission Nuclear Reactors
14.10 Nuclear Fusion in Astrophysical Environments
14.10.1 Fusion in Stars
14.10.2 Formation of Elements Heavier than Fe in Massive Stars
14.10.3 Earth and Solar System Dating
14.11 Nuclear Fusion in Laboratory
Appendix A
A.1 Periodic Table [P08]
A.2 The Natural Units in Subnuclear Physics
A.3 Basic Concepts of Relativity and Classical Electromagnetism
365
367
368
370
371
376
379
381
385
386
389
390
391
392
393
397
397
400
403
407
415
415
417
419
420
421
424
424
425
426
429
431
433
434
436
437
439
440
441
443
444
445
447
448
449
451
454
455
459
460
461
462
A.3.1 The Formalism of Special Relativity
A.3.2 The Formalism of Classical Electromagnetism
A.3.3 Gauge Invariance of the Electromagnetism
A.4 Dirac Equation and Formalism
A.4.1 Derivation of the Dirac Equation
A.4.2 General Properties of the Dirac Equation
A.4.3 Properties of the Dirac Equation Solutions
A.4.4 Helicity Operator and States
A.5 Physical and Astrophysical Constants [P08]
References
Index
462
464
466
467
467
469
472
475
478
481
487