Abstract
Webs are weighted sets of Feynman diagrams which build up the logarithms of correlators of Wilson lines, and provide the ingredients for the computation of the soft anomalous dimension. We present a general analysis of multiple gluon exchange webs (MGEWs) in correlators of semi-infinite non-lightlike Wilson lines, as functions of the exponentials of the Minkowski cusp angles, $\alpha_{ij}$, formed between lines $i$ and $j$. We compute a range of webs in this class, connecting up to five Wilson lines through four loops, we give an all-loop result for a special class of diagrams, and we discover a new kind of relation between webs connecting different numbers of Wilson lines, based on taking collinear limits. Our results support recent conjectures, stating that the contribution of any MGEW to the soft anomalous dimension is a sum of products of polylogarithms, each depending on a single cusp angle, and such that their symbol alphabet is restricted to $\alpha_{i j}$ and $1 - \alpha_{i j}^2$. Finally, we construct a simple basis of functions, defined through a one-dimensional integral representation in terms of powers of logarithms, which has all the expected analytic properties. This basis allows us to compactly express the results of all MGEWs computed so far, and we conjecture that it is sufficient for expressing all MGEWs at any loop order.
Highlights
Infrared singularities of scattering amplitudes in non-Abelian gauge theories are essential for understanding the physics of the strong interactions
We present a general analysis of multiple gluon exchange webs (MGEWs) in correlators of semi-infinite non-lightlike Wilson lines, as functions of the exponentials of the Minkowski cusp angles, αij, formed between lines i and j
We have extended the programme of refs. [14, 17, 20, 62], which established a diagrammatic approach for studying infrared singularities in QCD scattering amplitudes
Summary
Infrared singularities of scattering amplitudes in non-Abelian gauge theories are essential for understanding the physics of the strong interactions. The calculation of the logarithm of a Wilson-line correlator at a given order in perturbation theory proceeds by classifying the possible webs, identifying which connected colour factors they contribute to, and computing the corresponding kinematic integrals. The result is in complete agreement with the conjectured all-order properties of MGEWs. in section 7, we show that a specific class of highly symmetric diagrams contributing to n-line webs can be explicitly computed for any n, obtaining a remarkably simple result that further substantiates our conjectures. This all-order calculation of kinematic factors further allows us to prove that a specific colour structure arising from these webs has a vanishing coefficient for any n.
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