The role of colour flows in matrix element computations and Monte Carlo simulations

TL;DR

This paper explores how colour flow techniques can simplify matrix element calculations and improve Monte Carlo simulations by systematically including subleading-colour effects and unifying QCD and QED soft radiation patterns.

Contribution

It introduces a systematic approach to using colour flows for closed-form matrix element results and extends Monte Carlo accuracy beyond leading-colour effects.

Findings

Closed-form expressions for tree-level matrix elements using colour flows

Unified treatment of gluon and photon soft radiation patterns

Potential extension of Monte Carlo accuracy with subleading-colour effects

Abstract

We discuss how colour flows can be used to simplify the computation of matrix elements, and in the context of parton shower Monte Carlos with accuracy beyond leading-colour. We show that, by systematically employing them, the results for tree-level matrix elements and their soft limits can be given in a closed form that does not require any colour algebra. The colour flows that we define are a natural generalization of those exploited by existing Monte Carlos; we construct their representations in terms of different but conceptually equivalent quantities, namely colour loops and dipole graphs, and examine how these objects may help to extend the accuracy of Monte Carlos through the inclusion of subleading-colour effects. We show how the results that we obtain can be used, with trivial modifications, in the context of QCD+QED simulations, since we are able to put the gluon and photon soft-radiation patterns on the same footing. We also comment on some peculiar properties of gluon-only colour flows, and their relationships with established results in the mathematics of permutations.