  We compute the one-loop QCD amplitudes for the processes HqqQQ and Hqqgg, the
latter restricted to the case of opposite-helicity gluons. Analytic expressions
are presented for the color- and helicity-decomposed amplitudes. The coupling
of the Higgs boson to gluons is treated by an effective interaction in the
limit of large top quark mass. The Higgs field is split into a complex field
phi and its complex conjugate phi-dagger. The split is useful because
amplitudes involving phi have different analytic structure from those involving
phi-dagger. We compute the cut-containing pieces of the amplitudes using
generalized unitarity. The remaining rational parts are obtained by on-shell
recursion. Our results for HqqQQ agree with previous semi-numerical
computations. We also show how to convert existing semi-numerical results for
the production of a scalar Higgs boson into analogous results for a
pseudoscalar Higgs boson.
