Position-space cuts for Wilson line correlators

TL;DR

This paper advances the formalism for position-space cuts of eikonal diagrams, enabling direct computation of their discontinuities, and explores their relation to the cusp anomalous dimension and interquark potential.

Contribution

It introduces algorithms for position-space cuts of eikonal diagrams and applies them to multi-loop cases, confirming previous results and exploring theoretical implications.

Findings

Algorithms successfully compute diagram discontinuities.

Results agree with prior literature on two- and three-loop diagrams.

Discussion of the interplay between cuts and non-Abelian exponentiation.

Abstract

We further develop the formalism for taking position-space cuts of eikonal diagrams introduced in [Phys.Rev.Lett. 114 (2015), no. 18 181602, arXiv:1410.5681]. These cuts are applied directly to the position-space representation of any such diagram and compute its discontinuity to the leading order in the dimensional regulator. We provide algorithms for computing the position-space cuts and apply them to several two- and three-loop eikonal diagrams, finding agreement with results previously obtained in the literature. We discuss a non-trivial interplay between the cutting prescription and non-Abelian exponentiation. We furthermore discuss the relation of the imaginary part of the cusp anomalous dimension to the static interquark potential.