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 struc- tures 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.