Colour decompositions of multi-quark one-loop QCD amplitudes

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.