Towards Colour Flow Evolution at Two Loops

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.