Fiducial cross sections for Higgs boson production in association with a jet at next-to-next-to-leading order in QCD

We extend the recent computation of Higgs boson production in association with a jet through next-to-next-to-leading order in perturbative QCD by including decays of the Higgs boson to electroweak vector bosons. This allows us to compute fiducial cross sections and kinematic distributions including realistic selection criteria for the Higgs boson decay products. As an illustration, we present results for $pp \to H + j \to \gamma \gamma + j$ closely following the ATLAS 8 TeV analysis and for $pp \to H+ j \to W W + j \to e^+ \mu^- \nu \bar \nu + j $ in a CMS-like 13 TeV setup.