Soft Collinear Effective Theory

These lectures provide an introduction to Soft-Collinear Effective theory (SCET), the effective theory 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.

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 that there are strong constraints on the corresponding anomalous dimension.

This series of lectures was part of the workshop "The Infrared Structure of Gauge Theories" at ETH Zurich, February 1-12, 2010. The sildes are linked below.

  1. The strategy of regions
  2. Scalar SCET
  3. Generalization to QCD
  4. Resummation by RG evolution
  5. IR divergences of gauge theory amplitudes

Thomas Becher

ITP, University of Bern