Precise QCD predictions for the production of Higgs + jet final states.

We compute the cross section and differential distributions for the production of a Standard Model Higgs boson in association with a hadronic jet to next-to-next-to-leading order in quantum chromodynamics (QCD). In Higgs boson studies at the LHC, final states containing one jet are a dominant contribution to the total event rate, and their understanding is crucial for improved determinations of the Higgs boson properties. We observe substantial higher order corrections to transverse momentum spectra and rapidity distributions in Higgs-plus-one-jet final states. Their inclusion stabilises the residual theoretical uncertainty of the predictions around 9%, thereby providing important input to precision studies of the Higgs boson