Towards Colour Flow Evolution at Two Loops

TL;DR

This paper advances the calculation of soft gluon evolution at two loops by expressing colour structures in the colour flow basis, enabling improved resummation and parton shower algorithms beyond leading order and colour approximation.

Contribution

It introduces a method to compute two-loop and one-loop/one-emission contributions using the colour flow basis, revealing new correlations in virtual corrections.

Findings

Enables use in non-global observable resummation

Facilitates improved parton shower algorithms

Shows emergence of correlations beyond dipole picture

Abstract

We calculate the two-loop and one-loop/one-emission contributions required for soft gluon evolution at the next-to-leading order. The colour structures are expressed in the colour flow basis, and the kinematic dependence and loop integrals are expressed in terms of multiple cuts and phase-space-like integrals. This directly allows to use them in the resummation of non-global observables and improved parton shower algorithms beyond the leading order and beyond the leading colour limit. Within the colour flow basis it becomes apparent that correlations beyond a dipole picture emerge even in colour-diagonal elements of the virtual corrections.