  We consider a Higgs boson coupled to gluons via the five-dimensional
effective operator H Tr G_{munu}G^{munu} produced by considering the heavy top
quark limit of the one-loop coupling of Higgs and gluons in the standard model.
We treat H as the real part of a complex field phi that couples to the selfdual
gluon field strengths and compute the one-loop corrections to amplitudes
involving phi, two colour adjacent negative helicity gluons and an arbitrary
number of positive helicity gluons - the so-called phi-MHV amplitudes. We use
four-dimensional unitarity to construct the cut-containing contributions and
the recently developed recursion relations to obtain the rational contribution
for an arbitrary number of external gluons. We solve the recursion relations
and give explicit results for up to four external gluons. These amplitudes are
relevant for Higgs plus jet production via gluon fusion in the limit where the
top quark mass is large compared to all other scales in the problem.
