The colour evolution of the process q q -> q q g

TL;DR

This work addresses the calculation of the soft anomalous dimension matrix Λ for the 2→3 process $qq\to qqg$ within gaps-between-jets formalism. Using an eikonal one-loop analysis restricted to the interjet gap, the authors derive Λ in several colour bases and reveal a block-diagonal structure that separates qq→qq-like evolution from the 2→2 anomalous dimension Γ. They show how basis changes (including an s-channel projector basis) render the lower-right block equal to Γ and keep the soft matrix diagonal, aiding practical computations. The results provide a foundation for improved energy-flow analyses in 3-jet processes at the LHC and suggest that similar block structures may persist in more complex multi-jet processes, though full generalization to gg→ggg remains a challenge.

Abstract

We calculate the soft anomalous dimension matrix for a five-parton process, qq -> qqg. Considering different bases we unveil some interesting properties of this matrix.