Introduction

This two-week lecture series aims at presenting the most recent developements in the understanding of the infrared (IR) structure of gauge theories in perturbation theory. They main topics that will be covered will be the all-order analysis of IR singularities in gauge theories (Lorenzo Magnea), the Soft-Collinear Effective Theory (Thomas Becher), and an introduction to Monte Carlo event generators (Frank Krauss).

Lectures will be held in room HIT K 52. Click here for a map.

Program

1 Feb 11:00-12:45 Lorenzo Magnea Introduction to the IR problem in gauge theories and QCD
13:00-14:00 Welcome Apéro at HIT building, floor K
2 Feb 11:00-11:45 Frank Krauss The Monte Carlo principle
12:00-12:45 Parton level event generation
3 Feb 11:00-12:45 Thomas Becher Strategy of regions and effective theories in dimensional regularization
Exercises
4 Feb 11:00-11:45 Frank Krauss Dressing the Partons
12:00-12:45 Kingdoms of Modelling - Beyond Perturbation theory
5 Feb 11:00-12:45 Lorenzo Magnea IR and collinear singularities at one loop

8 Feb 11:00-11:45 Thomas Becher Soft-Collinear Effective Theory: scalar case
Exercises
12:00-12:45 Soft-Collinear Effective Theory: generalization to QCD
Exercises
9 Feb 11:00-12:45 Lorenzo Magnea All-order analysis of Feynman diagrams, IR power counting, factorization theorems
10 Feb 11:00-12:45 Thomas Becher Factorization and resummation by RG evolution
Exercises
11 Feb 11:00-12:45 Lorenzo Magnea Exponentiation of IR singularities in massless gauge theory amplitudes
12 Feb 11:00-12:45 Thomas Becher Towards n-jet processes: IR singularities of QCD amplitudes

Description of the Lectures

Lorenzo Magnea: "Soft and Collinear Gluons in Perturbative QCD"

I will give a general introduction to the problem of infrared and collinear singularities in perturbative QCD, explaining our current understanding and pointing to several applications. Specifically, I will discuss how singularities arise in Feynman diagram calculations, and how they are bypassed to build meaningful physical observables; I will introduce some of the technology needed to prove factorization theorems and to derive Sudakov resummations for physically interesting cross sections; I will describe some recent developments concerning the structure of singularities for general QCD amplitudes to all orders in perturbation theory.

Thomas Becher: "Soft-Collinear Effective Theory"

These lectures provide an introduction to Soft-Collinear Effective theory (SCET), the effective relevant for processes involving large energies and small invariant masses. SCET allows one to study soft-collinear factorization on the operator level and to resum logarithmically enhanced contributions to cross sections using RG evolution in the effective theory. In the first lecture, I will first discuss the strategy of regions technique to perform asymptotic expansions of loop integrals around various limits. There is a one-to-one correspondence between this method and effective theories in dimensional regularization. Based on this correspondence we then construct the effective Lagrangian and establish the power counting of the different fields. In the third lecture we'll apply the effective field theory to a problem with two directions of large momentum flow and illustrate how RG-evolution can be used to resum logarithmically enhanced contributions. In the last lecture, we discuss recent progress towards the analysis of processes with energetic partons in multiple directions. To perform resummations for such processes, one needs to understand the infrared singularities of n-point amplitudes. The effective theory treatment shows that these singularities can be analyzed with RG methods and there are strong constraints on the corresponding anomalous dimension.

Frank Krauss: "Introduction to event generators"

Basic principles in the construction of Monte Carlo event generators will be reviewed, ranging from technical considerations and methods to the actual physics of simulations in particle physics.

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