FYS3510–SubatomicPhysics
VS 2015
Farid Ould-Saada
Exam2016
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
Exampensum
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
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1.1 Introduction
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1.2 The Discovery of Particles
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1.3 The Concept of the Atom and Indivisibility
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1.4 The Standard Model of Microcosm – Fundamental Fermions and Bosons
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2 Particle Interactions with Matter and Detectors
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Emphasis in this chapter is on concepts and principles: how do various particles loose energy in
matter? How are particles detected?
2.1 Introduction
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2.2 Passage of Charged Particles Through Matter
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2.2.1 Energy Loss Through Ionization and Excitation
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2.2.2 “Classical” Calculation of Energy Loss Through Ionization
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2.2.3 Bremsstrahlung
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2.3 Photon Interactions
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2.3.1 Photoelectric Effect
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2.3.2 Compton Scattering
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2.3.3 Pair Production
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2.4 Electromagnetic Showers
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2.5 Neutron Interactions
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2.6 Qualitative Meaning of a Total Cross-Section Measurement
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2.7 Techniques of Particle Detection
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2.7.1 General Characteristics
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2.8 Ionization Detectors
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2.9 Scintillation Counters
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2.10 Semiconductor Detectors
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2.11 Cherenkov Counters
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2.12 The Bubble Chamber
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2.13 Electromagnetic and Hadronic Calorimeters
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3 Particle Accelerators and Particle Detection
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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?
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3.1.1 The Center-of-Mass (c.m.) System
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3.1.2 The Laboratory System
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3.1.3 Fixed Target Accelerator and Collider
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3.2 Linear and Circular Accelerators
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3.2.1 Linear Accelerators
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3.2.2 Circular Accelerators
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3.3 Colliders and Luminosity
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3.3.1 Example: the CERN Accelerator Complex
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3.4 Conversion of Energy into Mass
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3.4.1 Use of Fixed Target Accelerators
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3.4.2 Baryonic Number Conservation
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3.5 Particle Production in a Secondary Beam
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3.5.1 Time-of-Flight Spectrometer
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3.6 Bubble Chambers in Charged Particle Beams
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3.6.1 Conservation Laws
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3.6.2 The Electron “Spiral”
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3.6.3 Electron-Positron Pair
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3.6.4 An Electron-Positron “Tree”
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3.6.5 Charged Particle Decays
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4 The Paradigm of Interactions: The Electromagnetic Case
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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 Schrödinger 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
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4.7.1 Rutherford Scattering
4.7.2 The e+e-àµ+ µ - Process
4.7.3 Elastic Scattering e+e-àe+e- (Bhabha Scattering)
4.7.4 e+e-àγγAnnihilation
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
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
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7.10 Pseudoscalar Mesons
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7.11 The Vector Mesons
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7.12 Strangeness and Isospin Conservation
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7.13 The Six Quarks
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7.14 Experimental Tests on the Static Quark Model
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7.14.1 Leptonic Decays of Neutral Vector Mesons
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7.14.2 Lepton Pair Production
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7.14.3 Hadron-Hadron Cross-Sections at High Energies
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7.14.4 Baryon Magnetic Moments
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7.14.5 Relations Between Masses
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7.15 Searches for Free Quarks and Limits of the Model
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8 Weak Interactions and Neutrinos
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8.1 Introduction
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8.2 The Neutrino Hypothesis and the β Decay
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8.2.1 Nuclear β Decay and the Missing Energy
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8.2.2 The Pauli Desperate Remedy
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8.2.3 How World War II Accelerated the Neutrino Discovery
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8.3 Fermi Theory of Beta Decay
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8.3.1 Neutron Decay
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8.3.2 The Fermi Coupling Constant from Neutron β Decay
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8.3.3 The Coupling Constant ˛W from Fermi Theory
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8.4 Universality of Weak Interactions (I)
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8.4.1 Muon Lifetime
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8.4.2 The Sargent Rule
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8.4.3 The Puppi Triangle
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8.5 The Discovery of the Neutrino
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8.5.1 The Poltergeist Project
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8.6 Different Transition Types in β Decay
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8.6.1 The Cross-Section of the β-Inverse Process
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8.7 Lepton Families
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8.8 Parity Violation in β Decays
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8.9 The Two-Component Neutrino Theory
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8.10 Charged Pion Decay
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8.11 Strange Particle Decays
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8.12 Universality of Weak Interactions (II). The Cabibbo Angle
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8.13 Weak Interaction Neutral Current
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8.14 Weak Interactions and Quark Eigenstates
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8.14.1 The WI Hamiltonian and the GIM Mechanism
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8.14.2 Hints on the Fourth Quark fromWI Neutral Currents
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8.14.3 The Six Quarks and the Cabibbo–Kobayashi–MaskawaMatrix 218
8.15 Discovery of the W˙ and Z0 Vector Bosons
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8.16 The V-A Theory of CC Weak Interaction
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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
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8.16.2 Current–CurrentWeak Interaction
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9 Discoveries in Electron-Positron Collisions
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9.1 Introduction
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9.2 e+-e- Cross-Section and the Determination of the Number of Colors
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9.2.1 The Process e+e-àγàµ+µ232
9.2.2 The Color Quantum Number
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9.3 The Discovery of Charm and Beauty Quarks
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9.3.1 Mesons with c, c Quarks
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9.3.2 The J= Resonance Properties
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9.3.3 Mesons with b, b Quarks
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9.4 Spectroscopy of Heavy Mesons and αS Estimate
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9.5 The τ Lepton
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9.6 LEP Experiments and Examples of Events at LEP
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9.6.1 The LEP Detectors
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9.6.2 Events in 4π Detectors at LEP
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9.7 e+e- Collisions at Ecm ~91GeV. The Z0 Boson
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9.7.1 The Z0 Resonance
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9.7.2 Z0 Total and Partial Widths
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9.7.3 Measurable Quantities, Γinvis & Nber of Light Neutrino Families 251
9.7.4 Forward–Backward Asymmetries AFB
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9.7.5 Multihadronic Production Model
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9.8 e+e- Collisions for sqrt(s) > 100 GeV at LEP2
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9.8.1 e+e-àW+W-, Z0Z0 Cross-Sections
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9.8.2 The W Boson Mass and Width
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9.8.3 Measurement of αS
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9.8.4 The Higgs Boson Search at LEP
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10 High Energy Interactions and the Dynamic Quark Model
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10.1 Introduction
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10.2 Lepton–Nucleon Interactions at High Energies
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10.3 Elastic Electron-Proton Scattering
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10.3.1 Kinematic Variables
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10.3.2 Proton Form Factors
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10.4 Inelastic ep Cross-Section
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10.4.1 Partons in the Nucleons: Their Nature and Spin
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10.4.2 Electric Charge of the Partons
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10.5 Cross-Section for CC __N Interactions
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10.5.1 Comparison with Experimental Data
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10.5.2 The Neutrino-Nucleon Cross-Section
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10.6 “Naive” and “Advanced” Quark Models
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10.6.1 Q2-Dependence of the Structure Functions
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10.6.2 Summary of DIS Results
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10.7 High Energy Hadron-Hadron Collisions
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10.8 Total and Elastic Cross-Sections at High Energy
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10.8.1 Elastic Differential Cross-Sections
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10.8.2 Total Cross-Sections
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10.9 High Energy Inelastic Hadron Collisions at Low-pt
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10.9.1 Outline on High Energy Nucleus-Nucleus Collisions
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10.10 The LHC and the Search for the Higgs Boson
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10.10.1 Higgs Boson Production in pp Collisions
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10.10.2 Higgs Boson Decays
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10.10.3 Search Strategies at LHC
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11 The Standard Model of the Microcosm
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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
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11.2 Weak Interaction Divergences and Unitarity Problem
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11.3 Gauge Theories
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11.3.1 Choice of the Symmetry Group
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11.3.2 Gauge Invariance
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11.4 Gauge Invariance in the Electroweak Interaction
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11.4.1 Lagrangian Density of the Electroweak Theory
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11.5 Spontaneous Symmetry Breaking. The Higgs Mechanism
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11.6 The Weak Neutral Current
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11.7 The Fermion Masses
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11.8 Parameters of the Electroweak Interaction
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11.8.1 Electric Charge Screening in QED
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11.8.2 HO Feynman Diagrams, Mathematical Infinities and Renormalization in
QED
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11.9 The Strong Interaction
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11.9.1 Quantum Chromodynamics (QCD)
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11.9.2 Color Charge Screening in QCD
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11.9.3 Color Factors
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11.9.4 The Strong Coupling Constant αS
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11.10 The Standard Model: A Summary
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12 CP-Violation and Particle Oscillations
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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
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12.2 The K0K0bar System
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12.2.1 Time Development of a K0 Beam. K01 Regeneration.
Strangeness Oscillations
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12.3 CP-Violation in the K0-K0bar System
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12.3.1 The Formalism and the Parameters of CP-Violation
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12.4 What is the Reason for CP-Violation?
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12.5 CP-Violation in the B0-B0bar System
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12.5.1 Future Experiments
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12.6 Neutrino Oscillations
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12.6.1 The Special Case of Oscillations Between Two Flavors
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12.6.2 Three Flavor Oscillations
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12.6.3 The Approximation for a Neutrino with Dominant Mass
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12.6.4 Neutrino Oscillations in Matter
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12.7 Neutrinos from the Sun and Oscillation Studies
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12.8 Atmospheric __ Oscillations and Experiments
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12.8.1 Long Baseline Experiments
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12.9 Effects of Neutrino Oscillations
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13 Microcosm and Macrocosm
Lectures given at CERN on new physics can be found here: 2016 and 2015
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
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14 Fundamental Aspects of Nucleon Interactions
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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
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14.2 General Properties of Nuclei
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14.2.1 The Chart of Nuclides
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14.2.2 Nuclear Binding Energy
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14.2.3 Size of the Nuclei
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14.2.4 Electromagnetic Properties of the Nuclei
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14.3 Nuclear Models
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14.3.1 Fermi Gas Model
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14.3.2 Nuclear Drop Model
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14.3.3 Shell Model
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14.4 Properties of Nucleon-Nucleon Interaction
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14.5 Radioactive Decay and Dating
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14.5.1 Cascade Decays
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14.6 γ Decay
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14.7 α Decay
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14.7.1 Elementary Theory of α Decay
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14.7.2 Lifetime Calculation of the 238 92U Nucleus
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1
4.8 β Decay
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14.8.1 Elementary Theory of Nuclear β-Decay
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14.9 Nuclear Reactions and Nuclear Fission
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14.9.1 Nuclear Fission
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14.9.2 Fission Nuclear Reactors
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14.10 Nuclear Fusion in Astrophysical Environments
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14.10.1 Fusion in Stars
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14.10.2 Formation of Elements Heavier than Fe in Massive Stars
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14.10.3 Earth and Solar System Dating
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14.11 Nuclear Fusion in Laboratory
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“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
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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]
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A.2 The Natural Units in Sub-nuclear Physics
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A.3 Basic Concepts of Relativity and Classical Electromagnetism
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A.3.1 The Formalism of Special Relativity
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A.3.2 The Formalism of Classical Electromagnetism
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A.3.3 Gauge Invariance of the Electromagnetism
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A.4 Dirac Equation and Formalism
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Emphasis is on what was presented in the lectures (slides) / exercises.
A.4.1 Derivation of the Dirac Equation
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A.4.2 General Properties of the Dirac Equation
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A.4.3 Properties of the Dirac Equation Solutions
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A.4.4 Helicity Operator and States
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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]
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References
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Index
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