Cwebs beyond three loops in multiparton amplitudes

TL;DR

This paper completes the calculation of four-loop mixing matrices for Cwebs, which are essential for understanding soft gluon interactions in multiparton amplitudes, advancing precision in quantum chromodynamics calculations.

Contribution

It provides the full set of four-loop mixing matrices for Cwebs connecting two and three Wilson lines, including verification of the column sum rule and all-order results for certain classes.

Findings

All four-loop mixing matrices obey the column sum rule.

Low-dimensional mixing matrices can be uniquely determined from combinatorial properties.

Results complete the color structure needed for four-loop soft anomalous dimension calculations.

Abstract

Correlators of Wilson-line operators in non-abelian gauge theories are known to exponentiate, and their logarithms can be organised in terms of collections of Feynman diagrams called webs. In [1] we introduced the concept of Cweb, or correlator web, which is a set of skeleton diagrams built with connected gluon correlators, and we computed the mixing matrices for all Cwebs connecting four or five Wilson lines at four loops. Here we complete the evaluation of four-loop mixing matrices, presenting the results for all Cwebs connecting two and three Wilson lines. We observe that the conjuctured column sum rule is obeyed by all the mixing matrices that appear at four-loops. We also show how low-dimensional mixing matrices can be uniquely determined from their known combinatorial properties, and provide some all-order results for selected classes of mixing matrices. Our results complete the required colour building blocks for the calculation of the soft anomalous dimension matrix at four-loop order.