Introduction to QCD

Module PH2042

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

PH2042 is a semester module in English 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.

  • General catalogue of special courses
  • Specific catalogue of special courses for nuclear, particle, and astrophysics

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 75 h 5 CP

Responsible coordinator of the module PH2042 is Antonio Vairo.

Content, Learning Outcome and Preconditions


The lecture course will provide a basic introduction to the Quantumchromodynamics (QCD) and focus on its high energy (collider physics) and low energy (chiral perturbation theory) behaviour. The plan of the course is the following:

  • Strong interaction: historical overview and foundation of QCD
  • The QCD Lagrangian
    • SU(3) group and representations
    • Discrete symmetries: CPT
    • Continuous symmetries: gauge invariance
    • Gauge fixing and the Faddev-Popov ghost
    • QCD Lagrangian and Feynman rules
    • Exact symmetries and the θ term
    • Approximate symmetries
      • Isospin simmetry
      • Chiral simmetry
      • Heavy quark symmetry
  • Renormalization of QCD
    • Basics of dimensional regularization
      • The Adler-Bell-Jackiw anomaly in QCD
    • Renormalization and renormalization schemes
  • The running of α
    • The β function at one loop
    • Asymptotic freedom and dimensional transmutation
    • Confinement
      • The Wilson loop and the quark-antiquark static energy
    • Decoupling
  • QCD at high energies
    • e+e– → hadrons
      • Cross-section at LO
      • Threshold effects
      • Cross-section at NLO
      • Soft and collinear singularities
      • Bloch-Nordsieck and Kinoshita-Lee-Nauenberg theorems
      • Cross-section at higher orders and scale invariance
      • Jets, jet measures and event shape variables
    • Deep inelastic scattering
      • Kinematics
      • Structure functions
      • Bjorken limit and scaling
      • Parton distribution functions
      • Structure functions at NLO, splitting functions and scaling violation
      • DGLAP equations
  • QCD at low energies
    • Low-energy symmetries
      • Chiral symmetry and spontaneous symmetry breaking
      • Parity doubling, vector and axial vector spectral functions
      • Quark condensate
    • Low-energy degrees of freedom
      • Pions and kaons as Goldstone bosons
      • Non-linear realization of SU(Nf) X SU(Nf)
    • The chiral Lagrangian at order p²
      • Vector and axial vector currents
    • The chiral Lagrangian at order p² with a mass term
      • Gell-Mann Oakes Renner relations, Gell-Mann Okubo relation, light quark masses
    • The chiral Lagrangian at order p² with external fields
      • Coupling to electromagnetism and quark masses
    • π → μ ν and fπ
    • π π → π π

Learning Outcome

no info


Quantum Mechanics 1 + 2 and some basic knowledge of Quantum Field Theory

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 4 Introduction to quantum chromodynamics Vairo, A. Dienstag, 10:00–12:00
Donnerstag, 10:00–12:00

Learning and Teaching Methods

no info


Web page at



F. Wilczek QCD Made Simple, Phys. Today 53, August 22 (2000)

Running of α:

S. Bethke The 2009 World Average of α, Eur. Phys. J. C64 689, 2009


N. Brambilla and A. Vairo, Quark Confinement and the Hadron Spectrum, 13th Annual Hampton University Graduate Studies at the Continuous Electron Beam Facility, JLab, e-Print: hep-ph/9904330

S. Scherer, Introduction to Chiral Perturbation Theory, Adv. Nucl. Phys. 7:277,2003, e-Print: hep-ph/0210398


O. Nachtmann, Elementary Particle Physics, Springer Verlag 1989

F.J. Yndurain, The Theory of Quark and Gluon Interactions, Springer Verlag 1983

T. Muta, Foundations of Quantum Chromodynamics, World Scientific 1987

K. Huang, Quarks Leptons and Gauge Fields, World Scientific 1982

P. Pascual and R. Tarrach, QCD: Renormalization for the Practitioner, Springer Verlag 1984

R.K. Ellis, W.J. Stirling and B.R. Webber, QCD and Collider Physics, Cambridge University Press 1996

G. Sterman et al, Handbook of perturbative QCD

Y. Dokshitzer, V. Khoze, A. Mueller and S. Troyan, Basics of perturbative QCD

S. Pokorski, Gauge Field Theories (2nd Edition), Cambridge University Press 2000

Module Exam

Description of exams and course work

In an oral exam the learning outcome is tested using comprehension questions and sample problems.

In accordance with §12 (8) APSO the exam can be done as a written test. In this case the time duration is 60 minutes.

Exam Repetition

There is a possibility to take the exam at the end of the semester.

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