QCD

This lecture provides an introduction to Quantum Chromodynamics (QCD), the theory of the strong interaction between quarks and gluons. This non-abelian gauge theory gives rise to a wide range of different phenomena such as asymptotic freedom, confinement and chiral symmetry breaking. The course provides an introduction to QCD and the array of theoretical methods used to analyze this theory.

The lecture is suitable for master students with familiarity of basic quantum field theory. Part III of the lecture will start in week 8 of the semester, on November 4, and can serve as a graduate course. We should be able to hold the lecture in person, but please register on the course ILIAS page.

A few references are collected here. More will be added as the lecture progresses.

Part I: Basics

1. Introduction and overview
2. Gauge invariance, Lie group and algebra of SU(N), Yang-Mills theory
3. Faddeev-Popov Lagrangian (detailed derivation)
4. Feynman rules and group theory factors in diagrams
5. Renormalization
6. β-function and asymptotic freedom
7. Integrating out heavy quark flavors

Part II: Low-energy QCD

9. Chiral symmetry
10. Transformation properties of Goldstone boson fields
11. Chiral Perturbation Theory (CHPT)

Part III: QCD at colliders

14. e⁺ e⁻ → hadrons and the R-ratio (slides)
15. Higher-order corrections and IR divergences (Mathematica notebook for the computations: source and pdf.)
16. IR safety and jet cross sections
17. Operator analysis of the R-ratio
18. Soft factorization and soft effective theory in QED
19. Soft-Collinear Effective Theory (SCET)
20. Factorization for DIS

Exercises

• Exercise 1 (solutions)
• Exercise 2 (solution quark self energy, Mathematica notebook and PDF with all self-energies using Package X)
• Exercise 3 (solutions)
• Exercise 4 (solutions)
• Exercise 5 (solutions)
• Exercise 6 (solutions)
• Exercise 7 (solutions)
• Exercise 8 (solutions, Mathematica notebook and PDF with the NLO thrust computation.)
• Exercise 9 (solutions)
• Exercise 10 (solutions)