Webs in multiparton scattering using the replica trick

TL;DR

This paper generalizes the concept of webs in soft gluon exponentiation from two-parton to multi-leg processes, providing an all-orders combinatorial solution using the replica trick and deriving an algorithm for colour factors.

Contribution

It extends the web exponentiation framework to multi-leg scattering with non-trivial colour flow, introducing a new algorithm for colour factor computation.

Findings

Derived an all-orders solution for non-abelian exponentiation in multi-leg cases.

Developed an algorithm to compute colour factors for any diagram.

Showed how webs relate to partial cancellation of subdivergences.

Abstract

Soft gluon exponentiation in non-abelian gauge theories can be described in terms of webs. So far this description has been restricted to amplitudes with two hard partons, where webs were defined as the colour-connected subset of diagrams. Here we generalise the concept of webs to the multi-leg case, where the hard interaction involves non-trivial colour flow. Using the replica trick from statistical physics we solve the combinatorial problem of non-abelian exponentiation to all orders. In particular, we derive an algorithm for computing the colour factor associated with any given diagram in the exponent. The emerging result is exponentiation of a sum of webs, where each web is a linear combination of a subset of diagrams that are mutually related by permuting the eikonal gluon attachments to each hard parton. These linear combinations are responsible for partial cancellation of subdivergences, conforming with the renormalization of a multi-leg eikonal vertex. We also discuss the generalisation of exponentiation properties to beyond the eikonal approximation.