Collider Physics and QCD

This lecture provides an introduction to the physics at high-energy colliders, with special emphasis on QCD effects. Collider experiments are the main tool to study short-distance physics and the Large Hadron Collider is about to open a new window to the TeV scale. However, the prediction of collider processes is challenging: in order to be able to use perturbation theory, one has to define observables which are insensitive to low energy QCD effects, or use factorization theorems to separate high- and low energy physics. After an introduction to QCD, we will cover some of the theoretical issues in electron-positron, electron-hadron, and hadron-hadron scattering.

This lecture was given in the winter term 2009. The lecture notes are linked below. They are also available as a single file (250 pages, 14.6MB), which however does not contain the figures.

• Outline and some references
• 1. Introduction
• 2. Non-abelian gauge theory
  • 2.1 Gauge invariance
  • 2.2 The Yang-Mills Lagrangian
  • 2.3 Lie groups, SU(N)
  • 2.4 A brief history of QCD
• 3. Perturbative QCD
  • 3.1 The Faddeev-Popov Lagrangian
  • 3.2 Feynman rules
  • 3.3 Dimensional regularization
  • 3.4 From Green's functions to cross sections (figures)
  • 3.5 The β-function and the running of &alpha_s; (figures)
• 4. e⁺ e^- → hadrons
  • 4.1 e⁺ e^- → q q (figures)
  • 4.2 Soft and collinear divergences, IR safety
• 5. Operator product expansion in e⁺ e^-
  • 5.1 The optical theorem
  • 5.2 Operator analysis of e⁺ e^-
• 6. Event shapes and jets (figures)
  • 6.1 Event shape variables
  • 6.2 Jet algorithms
• 7. Soft-Collinear Effective Theory
  • 7.1 Strategy of regions
  • 7.2 Scalar SCET
  • 7.3 Generalization to QCD
    • 7.3.1 Wilson lines and decoupling transformation
• 8. Deep Inelastic Scattering (DIS)
  • 8.1 Factorization of the DIS cross section
  • 8.2 Parton Distribution Functions (Figures)
• 9. Hadron-hadron scattering
  • 9.1 Lepton pair production (Figures)
  • 9.2 Jet production (Introduction to MadEvent and Cross-section plots)
• 10. Parton shower and Monte Carlo methods
  • 10.1 Parton branching and splitting functions
  • 10.2 Parton shower
  • 10.3 Soft emissions and coherent branching

• Exercise 1, due Sept. 25.
• Exercise 2, due Oct. 9.
• Exercise 3, due Nov. 13.