Strong interactions and symmetries

Lecturers

• Jean-Marc Gerard
• Fabio Maltoni

Abstract

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).

Program

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

References

Basics

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

I Part : Non-perturbative aspects and symmetries

• ​Quantum Chromodynamics, by A.Pich.
• ​Electroweak interactions of hadrons, Acta Phys. Polon. B21:257-305,1990 J.M. Gerard.
• ​Weak Interactions, by Howard Georgi.

II Part : Perturbative QCD

• Introduction to QCD​, by M.L. Mangano.
• Introduction to QCD​, by P. Nason.
• Section 7.4, Chapters 15 and 16, and Sections 17.1 -> 17.4 of [P&S].

III Part : Advanced topics in PQCD

• QCD in e+e-​
• QCD in Deep Inelastic Scattering​
• QCD at hadronic colliders​
• Additional figures​

Exercises

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 ​http://madgraph.hep.uiuc.edu and send an e-mail to F.M. to get running access.

• Radiation from heavy quarks: the dead cone in $e^+e- \to Q \bar Q g$.
• Spin of the gluon: Vector vs scalar in the angular correlations of $ e^{+ e}- \to$ 4 jets.

• 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.

• Spin correlations in top decay.
• top production : $t \bar t$ production, Tevatron vs LHC.

• t' production : $t'$ production at the LHC.
• New resonances: Discover new resonances at the LHC.