Wilson-line geometries and the relation between IR singularities of form factors and the large-x limit of DGLAP splitting functions

TL;DR

This paper explores the connection between IR singularities in form factors and PDFs using Wilson-line correlators, revealing geometric differences in Wilson-line configurations and verifying results through two-loop calculations.

Contribution

It identifies the all-loop relation between the anomalous dimensions of form factors and PDFs via Wilson-line geometries, advancing understanding of IR singularities.

Findings

Relation between soft singularities of form factors and PDFs derived

Explicit two-loop diagrammatic calculations verify the theoretical relation

Classification of collinear singularities based on Wilson-line geometries

Abstract

We discuss the relation between the infrared singularities of on-shell partonic form factors and parton distribution functions (PDFs) near the elastic limit, through their factorisation in terms of Wilson-line correlators. Ultimately we identify the difference between the anomalous dimensions controlling single poles of these two quantities to all loops in terms of the closed parallelogram Wilson loop. To arrive at this result we first use the common hard-collinear behaviour of the two to derive a relation between their respective soft singularities, and then show that the latter is manifested in terms of differing Wilson-line geometries. We perform explicit diagrammatic calculations in configuration space through two loops to verify the relation. More generally, the emerging picture allows us to classify collinear singularities in eikonal quantities depending on whether they are associated with finite (closed) Wilson-line segments or infinite (open) ones.