Building blocks of Cwebs in multiparton scattering amplitudes

TL;DR

This paper introduces new concepts and a formalism for understanding the structure of Cwebs in multiparton scattering amplitudes, enabling predictions of exponentiated color factors and providing complete mixing matrices for certain classes.

Contribution

The paper develops a novel framework with concepts like normal ordering, Fused-Webs, and basis Cwebs, along with a Uniqueness theorem, to analyze and predict properties of Cwebs in gauge theories.

Findings

Complete mixing matrices for two classes of Cwebs are provided to all orders.

The formalism predicts the number of exponentiated color factors at higher orders.

New concepts simplify the understanding of Cweb structure and mixing matrices.

Abstract

The correlators of Wilson-line operators in non-abelian gauge theories are known to exponentiate, and their logarithms can be organised in terms of the collections of Feynman diagrams called Cwebs. The colour factors that appear in the logarithm correspond to completely connected diagrams and are determined by the web mixing matrices. In this article we introduce several new concepts: (a) Normal ordering of the diagrams of a Cweb, (b) Fused-Webs (c) Basis and Family of Cwebs. We use these ideas together with a Uniqueness theorem that we prove to arrive at an understanding of the diagonal blocks, and several null matrices that appear in the mixing matrices. We demonstrate using our formalism that, once the basis Cwebs present upto order $\alpha_{s}^{n}$ are determined, the number of exponentiated colour factors for several classes of Cwebs starting at order $\alpha_{s}^{n+1}$ can be predicted. We further provide complete results for the mixing matrices, to all orders in perturbation theory, for two special classes of Cwebs using our framework.