  We combine the six-dimensional helicity formalism of Cheung and O'Connell
with D-dimensional generalized unitarity to obtain a new formalism for
computing one-loop amplitudes in dimensionally regularized QCD. With this
procedure, we simultaneously obtain the pieces that are constructible from
four-dimensional unitarity cuts and the rational pieces that are missed by
them, while retaining a helicity formalism. We illustrate the procedure using
four- and five-point one-loop amplitudes in QCD, including examples with
external fermions. We also demonstrate the technique's effectiveness in
next-to-leading order QCD corrections to Higgs processes by computing the
next-to-leading order correction to the Higgs plus three positive-helicity
gluons amplitude in the large top-quark mass limit.
