The one-loop QCD corrections for γ∗ → qqgg

We compute the one-loop QCD amplitudes for the decay of an off-shell vector boson with vector couplings into a quark-antiquark pair accompanied by two gluons keeping, for the first time, all orders in the number of colours. Together with previous work this completes the calculation of the necessary one-loop amplitudes needed the calculation of the next-to-leading order O(αs3) corrections to four jet production in electron-positron annihilation, the production of a gauge boson accompanied by two jets in hadron-hadron collisions and three jet production in deep inelastic scattering.