Three-loop QCD corrections to the production of a Higgs boson and a jet

We compute three-loop QCD corrections to the scattering amplitude of a Higgs boson and three partons interfered with its tree level counterpart. Specifically, we derive our results in the generalized leading color limit. Our results are represented in terms of so-called multiple polylogarithms and thus are ready for use in phenomenological predictions. We provide the three-loop amplitudes necessary to compute the production cross section of a Higgs boson and a hadronic jet at hadron colliders and the decay probability of a Higgs boson to three hadronic jets at lepton colliders.