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

TL;DR

This work reformulates the gaps-between-jets non-global QCD problem in a color basis independent framework to derive the first super-leading logarithmic contribution. By expressing soft-gluon evolution with color operators and an anomalous-dimension matrix, it reveals that Coulomb gluon interactions cause a breakdown of naive real–virtual cancellation outside the gap and non-commuting color structures generate super-leading logs. The authors obtain explicit expressions for the first super-leading coefficient in qq, qg, and gg scatterings, including gluon-initiated processes, and validate results against previous calculations and independent color-algebra checks. The study points to broader implications for higher-order terms and potential strategies for resummation or observable design to manage these effects.

Abstract

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.

Figures (4)

• Figure 1: Factorization of soft gluon emission off a collinear bunch of partons. The cross indicates that the gluon can be attached to any other external leg. A sum over couplings to the final state collinear partons is implied.
• Figure 2: The relevant Feynman diagrams in the case that the out-of-gap (dotted) gluon is the hardest gluon. The dashed lines indicate soft (eikonal and Coulomb) gluons. Each subfigure represents three Feynman diagrams, corresponding to the three different ways of attaching the out-of-gap gluon. In diagrams (e) and (f) the soft gluon to the right of the cut should only be integrated over the region in which it has transverse momentum less than the out-of-gap gluon.
• Figure 3: The relevant Feynman diagrams in the case that the out-of-gap (dotted) gluon is the second hardest gluon. The dashed lines indicate soft (eikonal and Coulomb) gluons. Each subfigure represents three Feynman diagrams, corresponding to the three different ways of attaching the out-of-gap gluon. The soft gluon to the right of the cut should only be integrated over the region in which it has transverse momentum less than the out-of-gap gluon.
• Figure 4: The four diagrams that generate the colour matrix elements when the out-of-gap gluon is the hardest gluon. In the case that the out-of-gap gluon is next-to-hardest, only the first diagram contributes. The upper and lower loops can be quarks, anti-quarks or gluons. Note that these are not Feynman diagrams or even uncut diagrams; they represent only the colour factor of the final result. In the first diagram one of the original six gluon lines has been contracted away, resulting in the additional factor of $N_c$.