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Colorful Loops: Introduction to Quantum Chromodynamics and Loop Calculations

Module PH2267

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Basic Information

PH2267 is a semester module in English or German language at Master’s level which is offered in summer semester.

This Module is included in the following catalogues within the study programs in physics.

  • Specific catalogue of special courses for nuclear, particle, and astrophysics
  • Complementary catalogue of special courses for condensed matter physics
  • Complementary catalogue of special courses for Biophysics
  • Complementary catalogue of special courses for Applied and Engineering Physics
  • Specialization Modules in Elite-Master Program Theoretical and Mathematical Physics (TMP)

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
150 h 45 h 5 CP

Responsible coordinator of the module PH2267 is Gudrun Heinrich.

Content, Learning Outcome and Preconditions


  • QCD Lagrangian, Feynman Rules
  • Colour Algebra
  • Renormalisation Group and the QCD Beta Function
  • One-Loop Integrals
  • Next-to-Leading Order in Perturbation Theory
  • Soft and Collinear Singularities
  • From Amplitudes to Cross Sections
  • Parton Distribution Functions
  • Real Emission and Phase Space Integrals in Dimensional Regularisation
  • Techniques for Two-Loop Amplitudes and Integrals

Learning Outcome

After successful completion of the module the students are able to

  • understand Quantum Chromodynamics as a non-Abelian gauge field theory.
  • apply perturbation theory in the strong coupling.
  • know about methods to perform perturbative calculations.
  • know how to calculate simple processes at one-loop order.


No preconditions in addition to the requirements for the Master’s program in Physics.

PH2040 or equivalent basic knowledge of quantum field theory helpful.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

Learning and Teaching Methods

In the lectures the learning content is presented and illustrated with examples.

In the exercise the learning content is deepened by question and answer sessions and explicit calculations.

The problem examples are in the form of homework; solutions will be discussed bi-weekly in exercise groups.


Blackboard lecture, occasionally supplemented by slides

Script as PDF


  • M.E.Peskin, D.V.Schroeder, "Introduction to Quantum Field Theory", Addison-Wesley 1995.
  • G.Dissertori, I.Knowles, M.Schmelling, "Quantum Chromodynamics: High energy experiments and theory", International Series of Monographs on Physics No. 115, Oxford University Press, Feb. 2003. Reprinted in 2005.
  • T.Muta, "Foundations of QCD", World Scientific (1997).
  • J.Campbell, J.Huston and F.Krauss, "The Black Book of Quantum Chromodynamics: A Primer for the LHC Era" Oxford University Press, December 2017.
  • J.Wells and G.Altarelli, "Collider Physics within the Standard Model : A Primer", Lect. Notes Phys. 937 (2017) 1. doi:10.1007/978-3-319-51920-3.
  • V.A.Smirnov, "Feynman integral calculus", Springer, Berlin 2006.
  • V.A.Smirnov, "Analytic tools for Feynman integrals", Springer Tracts Mod. Phys. 250 (2012) 1.  doi:10.1007/978-3-642-34886-0.
  • L.J.Dixon, "Calculating scattering amplitudes efficiently", Invited lectures presented at the Theoretical Advanced Study Institute in Elementary Particle Physics (TASI '95): QCD and Beyond, Boulder, CO, June 1995.

Module Exam

Description of exams and course work

There will be an oral exam of 25 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using calculation problems and comprehension questions.

For example an assignment in the exam might be:

  • What is the physical origin of a soft divergence?
  • What is meant by "dimensional reduction"?
  • What does "asymptotic freedom" mean in QCD?

Exam Repetition

The exam may be repeated at the end of the semester.

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