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We consider a Higgs boson coupled to gluons via the five-dimensionaleffective operator H tr G_{\mu\nu}G^{\mu\nu}. We treat H as the real part of acomplex field phi that couples to the selfdual gluon field strengths andcompute the one-loop corrections to the phi-MHV amplitudes involving phi, twonegative helicity gluons and an arbitrary number of positive helicity gluons.Our results generalise earlier work where the two negative helicity gluons wereconstrained to be colour adjacent. We use four-dimensional unitarity toconstruct the cut-containing contributions and the recently developed recursionrelations to obtain the rational contribution for an arbitrary number ofexternal gluons. We solve the recursion relations and give explicit results forup to four external gluons. These amplitudes are relevant for Higgs plus jetproduction via gluon fusion in the limit where the top quark mass is largecompared to all other scales in the problem.

One-loop phi-MHV amplitudes using the unitarity bootstrap: the general helicity case