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Strong interactions and symmetries


  • Jean-Marc Gerard
  • Fabio Maltoni


This course aims at providing a first introduction to perturbative and non perturbative QCD. The prerequisites include Quantum Field Theory I and II, and Relativistic Quantum Mechanics. The course will be divided in three parts, for a total of 30+10 hours (5+1 ECTS).


I Part : Non-perturbative aspects and symmetries (J.-M. Gerard)

  • Perturbative vs non-perturbative approaches
  • Chiral symmetry and 1/Nc expansion
  • Effective Lagrangians and current algebra
  • U(1)_A problem and T invariance

II Part : Perturbative QCD (F. Maltoni)

  • Abelian and non-Abelian gauge invariance : formal and heuristic approaches
  • Ghosts and basics on the quantization of gauge theories
  • Feynman rules for QCD. Color algebra and its magic
  • Beta function in QCD : asymptotic freedom
  • e+ e- -> hadrons : LO (and NLO)
  • Infrared safety. Jets.

III Part : Advanced topics in pQCD (G. Soyez)

  • QCD in $e^{+}e^{-}$
    • $e^{+}e^{-}$ -> qqg: QCD divergences and various consequences
    • Event shapes, jets (cone, JADE, $k^t$)
  • QCD in Deep Inelastic Scattering
    • DIS kinematics, Parton Distribution Functions and Bjorken scaling
    • QCD radiation: scaling violations, factorisation theorem, DGLAP equation
  • QCD at hadronic colliders
    • PDF uncertainties
    • Drell-Yan and jets at LO
    • Multileg and NLO computations
    • jets



  • Cross sections and the S-matrix (Section 4.5 of Peskin and Schroeder [P&S])

I Part : Non-perturbative aspects and symmetries

II Part : Perturbative QCD

III Part : Advanced topics in PQCD


I Part

  • A list of exercises can be found here.
  • Take Home Project :
    • Calculation of the beta function in QCD.
    • Calculation of e+ e- -> hadrons at NLO in dimensional regularization.

II Part

QCD Phenomenology at colliders

Here is a list of exercises that can be "solved" using Software.MadGraph. To do so register at and send an e-mail to F.M. to get running access.

  • Drell-Yan : Study the rapidity asymmetry at the Tevatron.
  • Jets : Di-jet kinematics and rates in pp collisions.
  • 3 Jets : Energy distributions in 3-jet events.

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