Rings and strings: a basis for understanding subleading colour and QCD coherence beyond the two-jet limit

Guided by the colour-diagonal structure of collinear singularities, we identify a set of kinematic basis functions that are well suited to the simplification of soft gluon emission amplitudes. In particular, these basis functions, which emerge naturally in the colour flow basis, isolate the subleading colour contributions and improve the statistical convergence of the CVolver amplitude-evolution code. They also allow us to extend current angular-ordered parton showers beyond the azimuthally-averaged, two-jet limit