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

We consider a Higgs boson coupled to gluons via the five-dimensional effective operator H tr G_{\mu\nu}G^{\mu\nu}. 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 the phi-MHV amplitudes involving phi, two negative helicity gluons and an arbitrary number of positive helicity gluons. Our results generalise earlier work where the two negative helicity gluons were constrained to be colour adjacent. 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.