Module 1: Introduction, Relativistic Kinematics I, wxMaxima and Python

Description: Introduction to course. Using natural units (ℏ = 1, c = 1). Relativistic kinematics I. Basic Lorentz transformations for position and momentum; lifetime dilation and average decay distance of moving particles; Lorentz invariants; introduction to 4-vectors. Learning how to use wxMaxima and Python.

Readings and work

1. Read and evaluate the worksheet included in Introduction to natural units.
2. Read M&S Appendix A (P. 335-342) on relativistic kinematics.
3. Read the note Relativistic Kinematics I
4. Download and install wxMaxima.
5. Download and install Python (but first check to see if you already have it).
6. See the programming page for more information and tutorials for both languages.

Homework due

1. Do wxMaxima tutorial 1 and tutorial 2 on the programming page (see the pdf output there. Try some of your own calculations too.
2. Work through some of the Python tutorials.
3. Homework 1 due Friday, Aug. 30.

Module 2: Relativistic Kinematics II

Description: Transformation of angles and velocities; kinematics of 2-body decays using 4-vectors. Fixed target and colliding beam collisions; definition of Lab and CM frames for studying decay and scattering processes; definition of the variable s; minimum energy needed for particle production. Changing reference frames to simplify evaluation and solve problems. Applying relativistic kinematics to establish an approximate value of the GZK energy cutoff for intergalactic cosmic rays.

Readings and work

1. Read Relativistic Kinematics II
2. Two 2-body decay examples are worked out in twobody_test.py. Run this program. (You also need the file SM_constants.py which is imported by the other file.)
3. Try coding the top quark decay t --> W⁺ + b and print out the answers.
4. Please look at the numerical example in wxMaxima for the GZK cutoff showing the approximate calculation of the cutoff energy. The output is shown in this pdf file.
5. Read the articles about the GZK cosmic ray energy cutoff in Online materials.

Homework due

1. Work through wxMaxima tutorial 3 on the programming page.
2. Bonus question 1 due Monday, Sep. 9
3. Homework 2 due Monday, Sep. 9.
4. Bonus question 2 due Friday, Sep. 13
5. Homework 3 due Monday, Sep. 16.

Module 3: Introduction to the Standard Model

Description: Fundamental forces; definition of hadrons, mesons, baryons; introduction to quarks and leptons and their interactions; conservation laws; introduction to Feynman diagrams. Quark and lepton organization within three "generations", and evidence that they are fundamental point particles. Organization of the lowest mass spin 1/2 and spin 3/2 baryons.

Readings and work

• Read Sections 2.1-2.2 and Sections 3.1-3.4 in M&S.
• Read pp. 1-28 in the Subatomic Zoo book. There are some worthwhile examples here.
• Read Sections 3.5-3.6 in M&S.
• Read pp. 29-70 in the Subatomic Zoo book. There are many good examples which help clarify our more advanced discussion.

Homework due

Module 4: Quark model and hadron properties

Description: Detailed discussion of mesons and baryons; Spin 0 and spin 1 mesons; spin 1/2 and spin 3/2 baryons; decays of hadrons via strong, electromagnetic and weak interactions and their lifetimes and widths; partial width and total width; dependence of lifetime on total width; relative strengths of strong, weak and electromagnetic interactions and effect on lifetimes

Discussion of allowed and forbidden decays; lepton violations, baryon violations, angular momentum non-conservation (half-integral vs integral); energy non-conservation; need for weak decays when quark flavor (flavor = strange, charm, bottom, top) must be violated; ultimate final states for any baryon decay.

Decays of the spin 3/2 baryons (strong decays); special case of the Ω⁻ baryon; relative strengths of strong, weak and electron and quantitative effect on lifetimes; masses and magnetic moments in the quark model and comparison with experimentally measured values. Electromagnetic mass splittings within baryon multiplets and determination of coulomb effects and m_d - m_u mass difference.

Readings and work

• Read the short note on the light mesons and baryons, showing how their masses lie in multiplets which differ in strangeness. The lifetimes of the particles are shown, clearly showing patterns where the heavier particles decay strongly and the lighter ones decay weakly.
• Read the brief note on magnetic moments in the quark model.

Homework due

1. Bonus question 3 due Friday, Sep. 20
2. Homework 4 due Monday, Sep. 23

Module 5: Overview of quantum mechanics

Description: Operators, Schrodinger equation, stationary states, eigenvalues and eigenstates, expectation values, free particle and particle in a 1-D box. Three dimensional Schrodinger equation, free particle in three dimensions, three dimensional particle in a box and energy levels, hydrogen atom solutions. Uncertainty principle; applied to particle in a box; applied to finding the size of an atom.

Readings and work

• My modified version of Korytov's summary note on QM (deprecated).
• This QM Basics document provides a summary of QM that you need for this course.
• Please read M&S Chap. 6.1-6.3 on the quark model and light hadrons.

Homework due

• Homework 5, due Monday, Sep. 30
• Bonus question 4, due Friday Oct. 4

Module 6: Scattering basics: cross section, flux and luminosity. Also covered are particle width, lifetime and branching fractions.

Description: Basic concepts of scattering, cross section, flux and luminosity, integrated luminosity, differential cross section. Example using LHC running conditions.

Readings and work

1. Read the writeup on cross sections, flux and luminosity.

Homework due

Module 7: Scattering in QM

Description: Calculating scattering rates and decay rates in QM using Fourier transform of potential; definition of matrix element; comparison of strong, E&M and weak scattering rates; coupling constants; Rutherford scattering and dσ/dΩ formula. Introduction to delta function δ(x - a). Particle lifetime, relationship of lifetime and width, resonance shape.

Scattering with heavy particle exchange; calculating total cross section with heavy particle exchange; calculating scattering amplitudes (identifying vertex factors and propagators); example of neutrino-nucleon scattering in weak interactions showing effect of W exchange on the cross section; interference when two or more processes contribute to the same final state.

Why the weak interaction is so weak (heavy virtual particle exchange); universality of weak coupling strength to leptons and its experimental verification via precision measurements.

Readings and work

• Read note on Scattering in QM.
• Read the writeup on particle widths, lifetime and branching fractions.
• Read Subatomic Zoo pp. 71-80.

Homework due

Module 8 : Physics of particle accelerators

Description: Brief history: Cockcroft-Walton; Van de Graaff; linear accelerators; cyclotrons; phase stability and synchrocyclotrons; weak focusing and synchrotrons; strong focusing and large synchrotrons; colliders. Examples of accelerators.

Discussion of magnets and bending radius. Comparison of fixed target and colliding beam accelerators wrt center of mass energy and luminosity. Discussion of e⁺e⁻ storage rings, pp and pp colliders, and the ep collider at HERA.

Synchrotron radiation and RF power; limitations on circular e⁺e⁻ accelerators due to synchrotron radiation and comparison with pp colliders. The planned International Linear Collider (ILC) for next generation ultra-high energy e⁺e⁻ collisions. Discussion of the LHC bunch structure and live statistics.

Readings and work

• Read Korytov note 9 about accelerators.
• Read Subatomic Zoo pp. 81-91.
• Nice 6-minute video "From bottle to bang" showing how protons are taken from a hydrogen bottle and accelerated in several stages until they finish their journey in the LHC colliding rings.
• PDF file showing integrated and daily luminosity (in pb^-1) at CMS.
• Read note on synchrotron radiation.

Homework due

• Homework 6, due Monday, Oct. 14 (changed from Oct. 11)
• Bonus question 5, due Monday, Oct. 14

Module 9: Detectors and experiments

Description: Measuring the properties of high energy collisions by detecting long-lived particles. Decay lengths of the long-lived particles. Searching for new particles by making plots of invariant mass and examples of invariant mass plots in CMS.

Interactions of particles with matter; ionization of charged particles; bremsstrahlung and pair production; showering of electrons, photons and hadrons.

Charged particle tracking measurements and a quantitative look at momentum errors. Cerenkov radiation and dE/dx measurements for charged particle identification. Electromagnetic and hadronic showers and identification of electrons, photons and hadrons. Penetrating particles and muon identification; neutrino detectors.

Readings and work

• Event dump showing a simulated pp → Z⁰ + X, Z⁰→μ⁺μ⁻ event and has an explanation of the different columns.
• These event displays (1 and 2) show a top quark decaying via t → be⁺ν_eand t → bμ⁺ν_μ, where the b quark decays are tagged by a displaced vertex.
• Several two particle invariant mass histograms showing peaks at the K_S, Λ⁰, Ξ⁻, ψ, Υ, B⁻ masses. Identifying peaks in the invariant mass histogram of two or more particles is the primary way we identify new particles.
• Read M&S Chapter 3 in which this material is discussed.
• Read Subatomic Zoo pp. 92-107.
• Read "Charge Particle Measurement and Identification".
• Please read the Korytov note on particle interactions with matter, which summarizes most of this work.

Homework due

• Homework 7, due Wednesday, Oct. 23.
• Bonus problem 6, due Wednesday, Oct. 23

Module 10: Probability and statistics

Description: Probability distributions; calculation of mean, variance, standard deviation; properties of most common distributions (Gaussian, Poisson, exponential); propagation of errors when adding/subtracting, multiplying/dividing and taking powers.

Using the Poisson distribution to estimate probabilities of obtaining a specified count range; upper limits, determination of mean and standard deviation from a sample.

Optimal combination of measurements to minimize error; real world examples of statistical and systematic errors in experiments.

Readings and work

• Read Useful Statistics for Data Analysis.

Homework due

Module 11: e⁺e⁻physics

Description: Discussion of R and its dependence on QCD colors; dσ/dΩ for e⁺e⁻ → μ⁺μ⁻ and jets, showing classic 1+cos²(θ) behavior. QCD first order correction to R.

Production of heavy cc resonances (J/ψ, ψ(2S), ψ(3770), η_c, χ_c), bb resonances (Υ(1S), Υ(2S), Υ(3S), Υ(4S)) and mesons and baryons with a c quark or a b quark. B factories at KEK and SLAC and precision measurements of B decays and CP violation.

Introduction to the general resonance formula and its applicability to e⁺e⁻ resonances.

Precision measurements of e⁺e⁻ → Z⁰ and verification of Standard Model. Interference effects in scattering: γ and Z⁰ exchange contributing to e⁺e⁻ → f⁺f⁻(f = fermion). Detailed discussion of asymmetries in e⁺e⁻ → f⁺f⁻at the Z⁰, comparing different species of f, using experimental data from LEP. Detailed discussion of Z⁰ width and the determination of the number of quark/lepton generations.

Readings and work

1. M&S Section 6.4 (pp. 168-175)
2. M&S Section 7.1-7.2 (pp. 179-196)

Homework due

Module 12: Weak interaction physics

Description: Definition of charged and neutral weak currents; why the weak interaction is so weak (heavy virtual particle exchange); universality of weak coupling strength to leptons and its experimental verification; charged weak coupling of quarks; Quark mixing in charged weak interactions; introduction to CKM matrix and its experimental confirmation; CP violation.

Readings and work

1. Charged weak currents: M&S Sections 8.1-8.2 (pp. 217-245)
2. Electroweak unification: M&S Sections 9.1-9.2 (pp. 249-276)

Homework due

Module 13: Collider physics at the LHC

Description: Recent measurements at LHC, including the Higgs discovery in July 2012.

Readings and work

Homework due

Module 14: Student presentations

Description: Presentation of student research projects.