A simple introduction to soft resummation

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.

Figures (8)

• Figure 1: The leading-order Drell-Yan production process (left) and a next-to-leading order real gluon emission correction to it (right).
• Figure 2: Radiation of a gluon with momentum $k$ from a quark with momentum $p$.
• Figure 3: The leading order Drell-Yan process and the first-order real-emission corrections to it.
• Figure 4: Cancellation of infrared singularities: the interference between the leading-order process (a) and the loop correction (b) cancels the infrared singularity arising due to interference between the two real-emission contributions (c) and (d).
• Figure 5: Kinematics of multiple emission.