Theoretical Methods for QCD at Colliders

This course provides an introduction to Quantum Chromodynamics (QCD) focusing on theoretical methods to study its pertubative aspects and their application to the physics of hadron colliders like the LHC. Starting from the idea of collinear factorization, the course will introduce the main theoretical ideas required to study and model high energy scattering processes with high precision at hadron colliders, by applying them explicitly to the Drell-Yan process and to Higgs production in gluon fusion at the LHC. The main topics covered will be:

1. The QCD Lagrangian, quantization and Feynman rules 
2. Asymptotic freedom and (collinear) factorization
3. QCD calculations at Leading Order (LO), spinor helicity formalism
4. Virtual corrections: modern methods for (multi) loop calculations
5. Real corrections: Infrared singularities and their subtraction to NLO
6. Parton evolution and Parton distributions functions (PDFs)
7. Basics of resummation
8. If time permits: basics of parton showers

After successful completion of the module the students are able to understand and model processes that happen at hadronic colliders. For example the students will be able to

1. Compute tree-level and one-loop amplitudes in QCD
2. Describe the parton model and parton evolution in perturbative QCD
3. Describe the pattern of infrared singularities in QCD up to NLO
4. Model the transverse momentum distribution of a colorless final state at the LHC 
5. Understand the theoretical ideas behind precision calculations for hadron colliders beyond LO

The course will assume some familiarity with standard ideas described in Quantum Field Theory 1 (Feynman rules in QED, basics of scattering amplitudes and cross-sections)

Blackboard frontal lectures and tutorials

Blackboard lectures, possibly but not necessarily with use of slides to show complicated results

• Lectures on LHC Physics, T. Plehn, https://arxiv.org/abs/0910.4182
• QCD and Collider Physics, R.K. Ellis, W.J. Stirling and B.R. Webber
• Quantum Chromodynamics, G. Dissertori, I.G. Knowles, M. Schmelling
• Collider Physics within the Standard Model, G. Altarelli

There will be an oral exam of 30 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 and sample calculations.

For example an assignment in the exam might be:

• Describe the origin of IR divergences in QCD
• Explain the basics of resummation
• Compute a simple QCD amplitude
• Describe parton evolution

Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.