On the renormalization of multiparton webs

TL;DR

This paper explores the renormalization of multiparton webs in soft-gluon exponentiation, deriving constraints on web poles, analyzing multi-loop singularities, and proposing a new conjecture for web mixing matrices to advance understanding of non-Abelian exponentiation.

Contribution

It establishes renormalization constraints for webs, relates diagrammatic and renormalization approaches, and introduces a new conjecture for web mixing matrices, advancing multiparton amplitude analysis.

Findings

Renormalization constraints relate web poles to lower-order webs.

Explicit analysis of singularities up to four loops.

Proposed a new conjecture for web mixing matrices.

Abstract

We consider the recently developed diagrammatic approach to soft-gluon exponentiation in multiparton scattering amplitudes, where the exponent is written as a sum of webs - closed sets of diagrams whose colour and kinematic parts are entangled via mixing matrices. A complementary approach to exponentiation is based on the multiplicative renormalizability of intersecting Wilson lines, and their subsequent finite anomalous dimension. Relating this framework to that of webs, we derive renormalization constraints expressing all multiple poles of any given web in terms of lower-order webs. We examine these constraints explicitly up to four loops, and find that they are realised through the action of the web mixing matrices in conjunction with the fact that multiple pole terms in each diagram reduce to sums of products of lower-loop integrals. Relevant singularities of multi-eikonal amplitudes up to three loops are calculated in dimensional regularization using an exponential infrared regulator. Finally, we formulate a new conjecture for web mixing matrices, involving a weighted sum over column entries. Our results form an important step in understanding non-Abelian exponentiation in multiparton amplitudes, and pave the way for higher-loop computations of the soft anomalous dimension.