Colour Decompositions of Multi-quark One-loop QCD Amplitudes

TL;DR

This paper presents a new method for decomposing one-loop QCD amplitudes into colour-ordered components, enabling more efficient calculations of high-multiplicity scattering processes relevant for collider physics.

Contribution

It introduces novel expressions for colour structure coefficients using primitive amplitudes and reveals relations that optimize NLO QCD computations.

Findings

Derived new expressions for colour coefficients in multi-quark amplitudes.

Identified relations between primitive amplitudes to improve computational efficiency.

Computed the full-colour virtual contribution for W+4-jet production at the LHC.

Abstract

We describe the decomposition of one-loop QCD amplitudes in terms of colour-ordered building blocks. We give new expressions for the coefficients of QCD colour structures in terms of ordered objects called primitive amplitudes, for processes with up to seven partons. These results are needed in computations of high-multiplicity scattering cross sections in next-to-leading-order (NLO) QCD. We explain the origin of new relations between multi-quark primitive amplitudes which can be used to optimise efficiency of NLO computations. As a first application we compute the full-colour virtual contribution to the cross section for W+4-jet production at the Large Hadron Collider, and verify that it is very well approximated by keeping only the leading terms in an expansion around the formal limit of a large number of colours.