Color structure for soft gluon resummation - a general recipe

TL;DR

This work tackles the complexity of soft gluon resummation in multi-parton QCD by introducing a general, non-orthogonal color basis inspired by the Nc→∞ limit. The proposed basis ensures that gluon exchanges map directly to linear combinations of a small set of basis tensors, avoiding expensive scalar-product decompositions during each exchange. The authors demonstrate the method with explicit recalculations of soft anomalous dimension matrices for gg→gg, qq̄→qq̄g, and qq̄→ggg, showing a leading diagonal structure in the large-Nc limit and substantial computational sparsity. The approach offers a practical path toward incorporating non-leading color effects in event generators and may extend to higher-loop and non-global log analyses in multi-parton QCD.

Abstract

A strategy for calculating the color structure needed for soft gluon resummation for processes with any number of colored partons is introduced using a N_c --> infinity inspired basis. In this basis a general formalism can be found at the same time as the calculations are simplified. The advantages are illustrated by recalculating the soft anomalous dimension matrix for the processes gg --> gg, q\qbar --> q \qbar g and q\qbar --> ggg.