One-loop φ-MHV amplitudes using the unitarity bootstrap

We consider a Higgs boson coupled to gluons via the five-dimensional effective operator HtrGμνGμν 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 φ that couples to the selfdual gluon field strengths and compute the one-loop corrections to amplitudes involving φ, two colour adjacent negative helicity gluons and an arbitrary number of positive helicity gluons - the so-called φ-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. © SISSA 2007.