We present the one-loop helicity amplitudes for processes involving a vector boson V (V=W,Z, or gamma^*) and four massless quarks, 0 to V q-bar q Q-bar Q, where V couples to a massless lepton pair. These amplitudes are required for next-to-leading order O(alpha_s^3) numerical programs for four-jet production at e^+ e^- colliders, for W, Z or Drell-Yan production in association with two jets at hadron colliders, and for three-jet production in deeply inelastic scattering experiments. We obtained the amplitudes presented here by using their analytic properties to constrain their form.
@article{arxiv.hep-ph/9610370,
title = {One-Loop Amplitudes for e^+ e^- to q-bar q Q-bar Q},
author = {Z. Bern and L. Dixon and D. A. Kosower and S. Weinzierl},
journal= {arXiv preprint arXiv:hep-ph/9610370},
year = {2014}
}