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

Colour Decompositions of Multi-quark One-loop QCD Amplitudes