Infrared divergences and non-lightlike eikonal lines in Sudakov processes

TL;DR

The paper addresses infrared contributions in non-inclusive, multi-scale QCD processes by proposing a systematic, integrand-level subtraction method inspired by renormalization. It defines region-specific counterterms from gauge-invariant Wilson lines along non-lightlike directions, yielding soft ($S$), collinear ($A$, $B$), and hard ($H$) contributions that reproduce the one-loop Sudakov form factor at leading power while remaining infrared-safe. The approach provides simple evolution in rapidity variables and clarifies the sources of power corrections, facilitating higher-order generalizations and numerical applications. This framework has potential impact on factorization proofs and on improving event generators for multi-scale QCD processes.

Abstract

We propose a method to analyze infrared contributions to non-inclusive processes in QCD. We use the one-loop Sudakov form factor as a working example. Borrowing techniques from renormalization theory, we construct counterterms for the contributions from the soft and collinear regions, and we relate them to eikonal Wilson lines taken along non-lightlike directions.

Figures (1)

• Figure 1: (a) Form factor graph; (b) soft and collinear regions.