Analytic one-loop amplitudes for a Higgs boson plus four partons

We compute the one-loop QCD amplitudes for the processes H q-bar q Q-bar Q and H q-bar qgg, 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 φ and its complex conjugate φ†. The split is useful because amplitudes involving φ have different analytic structure from those involving φ†. 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 H q-bar q Q-bar Q 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.