A simple introduction to soft resummation

TL;DR

This paper offers an accessible introduction to soft resummation techniques in QCD, emphasizing practical methods and fundamental concepts like factorization and renormalization group invariance.

Contribution

It provides a pedagogical overview of soft resummation, including derivations from infrared singularity cancellation and simplified explanations of related QCD concepts.

Findings

Derivation of threshold resummation from renormalization group arguments

Explanation of factorization of infrared and collinear singularities

Brief overview of transverse momentum resummation techniques

Abstract

We provide an elementary pedagogical introduction to some basic concepts and techniques of soft (or Sudakov) resummation, specifically in QCD, paying particular attention to simple but useful tricks of the trade. We briefly review collinear (Altarelli-Parisi) and infrared (eikonal)factorization, cancellation of infrared singularities and factorization of mass singularities. We recall basic concepts on renormalization group invariance and the solution of renormalization group equations. We then show how threshold resummation can be derived from a renormalization group argument following from the cancellation of infrared singularities. We discuss various equivalent forms of the resummed result, and we briefly present transverse momentum resummation.