Introduction to QCD

The lecture 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 contents are as follows:

• 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

After successful completion of the module the students are able to:

• Write the QCD Lagrangian and its Feynman rules
• Describe its symmetries and degrees of freedom
• Discuss the renormalization of QCD and compute the one loop running coupling constant
• Compute the LO e+e- -> hadrons cross section
• Explain what jets are and their basic properties
• Describe the DIS, define PDF and derive the DGLAP equations
• Introduce chiral perturbation theory
• Derive basic equalities in chiral perturbation theory
• Compute pion decays and scatterings

Quantum Mechanics 1 + 2 (PH0007 and PH1002) and some basic knowledge of Quantum Field Theory.

The blakboard lectures aim at introducing the students to the subject in a step by step approach where every result is carefully derived and consistently justified. Plenty of examples are presented. Figures and results are kept updated and reflect the status of the art. Further possible development beyond the Standard Model are suggested. Students are encouraged to participate actively in the lecture and encouraged to keep a critical open mind on the subject.

Blackboard, Powerpoint, webpage http://users.ph.tum.de/gu32tel/Lectures/WS18-19-QCD.html

Invitation:

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)

Lectures:

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

Books:

• O. Nachtmann, A. Lahee & W. Wetzel: Elementary Particle Physics: Concepts and Phenomena, Springer Verlag, (1989)
• F.J. Yndurain: The Theory of Quark and Gluon Interactions, Springer Verlag, (1983)
• T. Muta: Foundations of Quantum Chromodynamics, World Scientific, (2009)
• K. Huang: Quarks Leptons and Gauge Fields, World Scientific, (1982)
• P. Pascual & R. Tarrach: QCD: Renormalization for the Practitioner, Springer Verlag, (1984)
• R.K. Ellis, W.J. Stirling & B.R. Webber: QCD and Collider Physics, Cambridge University Press, (2010)
• G. Sterman: Handbook of perturbative QCD, CTEQ Collaboration, (1993)
• Yu.L. Dokshitzer, V.A. Khoze, A.H. Mueller & S.I. Troyan: Basics of perturbative QCD, Edition Frontières, (1991)
• S. Pokorski: Gauge Field Theories (2nd Edition), Cambridge University Press, (2000)

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 comprehension questions ans sample calculations.

For example an assignment in the exam might be:

• Write the QCD Lagrangian and its Feynman rules.
• What is meant with asymptotic freedom?
• What are the experimental evidences for 3 colors?
• Define jets.
• Write the LO chiral lagrangian.