Les Houches Lectures on Soft-Collinear Effective Theory

TL;DR

The notes provide a structured introduction to Soft-Collinear Effective Theory (SCET), detailing its conceptual basis, the role of Wilson coefficients, and the operator formalism for factorization and resummation. Starting from soft-effective theory in QED and progressing through the construction of soft and collinear sectors, the text derives a leading-power SCET Lagrangian and current operators, and demonstrates how RG evolution resums large logarithms in jet-related observables. Key contributions include explicit factorization theorems for thrust and jet cross sections, the handling of Sudakov and nonglobal logarithms, and connections to parton showers and modern subtraction schemes. The framework highlights the practical impact of SCET in precision collider predictions, enabling systematic resummations and providing a path toward automation and advanced jet-substructure analyses.

Abstract

These lectures provide an introduction to Soft-Collinear Effective Theory. As applications we discuss resummation for (i) soft-photon effects in QED, (ii) event-shape variables and (iii) jet cross sections.

Figures (15)

• Figure 1: Sketch of a two jet process.
• Figure 2: Electron-electron scattering, including soft-photon radiation.
• Figure 3: Soft emissions from an outgoing electron. Note that $q'=k+k'$ and $q=k$.
• Figure 4: QED tree-level diagrams for the matching computation needed to extract the Wilson coefficient \ref{['Lint']}.
• Figure 5: Loop correction on an a fermion line.