Position-space cuts for Wilson line correlators

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.

39+18 pages, 16 figures; elaborated the discussion of the comparison of numerical and analytic results for the three-gluon vertex diagram in the caption of fig. 16; version to be published in JHEP

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• Coordinate light-cone-ordered perturbation theory