Super-leading logarithms in non-global observables in QCD: colour basis independent calculation

In a previous paper we reported the discovery of super-leading logarithmic terms in a non-global QCD observable. In this short update we recalculate the first super-leading logarithmic contribution to the `gaps between jets' cross-section using a colour basis independent notation. This sheds light on the structure and origin of the super-leading terms and allows them to be calculated for gluon scattering processes for the first time.