Imaginary parts and discontinuities of Wilson line correlators

TL;DR

This paper develops a position-space cutting rule for Wilson line correlators that directly computes their imaginary parts, providing an analog to momentum-space Cutkosky rules with specific constraints on exchanged gauge bosons.

Contribution

It introduces a novel position-space cut prescription for Wilson line diagrams, enabling direct calculation of imaginary parts in a way analogous to momentum-space methods.

Findings

Position-space cuts compute the imaginary part at leading order.

The method constrains gauge bosons to be lightlike, affecting the imaginary part.

Different behavior for space- and timelike kinematics was observed.

Abstract

We introduce a notion of position-space cuts of eikonal diagrams, the set of diagrams appearing in the perturbative expansion of the correlator of a set of straight semi-infinite Wilson lines. The cuts are applied directly to the position-space representation of any such diagram and compute its imaginary part to the leading order in the dimensional regulator. Our cutting prescription thus defines a position-space analog of the standard momentum-space Cutkosky rules. Unlike momentum-space cuts which put internal lines on shell, position-space cuts constrain a number of the gauge bosons exchanged between the energetic partons to be lightlike, leading to a vanishing and a non-vanishing imaginary part for space- and timelike kinematics, respectively.