The colour matrix at next-to-leading-colour accuracy for tree-level multi-parton processes

TL;DR

This paper analyzes the next-to-leading-colour contributions to the colour matrix in tree-level multi-parton processes, revealing a polynomial scaling that enables more efficient matrix element generation without factorial complexity.

Contribution

It identifies the non-zero elements of the NLC colour matrix and demonstrates polynomial scaling, facilitating accurate and efficient tree-level matrix element computations.

Findings

Non-zero NLC colour matrix elements identified

Scaling reduces from factorial to polynomial

Enables efficient matrix element generation

Abstract

We investigate the next-to-leading-colour (NLC) contributions to the colour matrix in the fundamental and the colour-flow decompositions for tree-level processes with all gluons, one quark pair and two quark pairs. By analytical examination of the colour factors, we find the non-zero elements in the colour matrix at NLC. At this colour order, together with the symmetry of the phase-space, it is reduced from factorial to polynomial the scaling of the contributing dual amplitudes as the number of partons participating in the scattering process is increased. This opens a path to an accurate tree-level matrix element generator of which all factorial complexity is removed, without resulting to Monte Carlo sampling over colour.