We present the computation of Higgs boson production in association with a jet at the LHC including QCD corrections up to NNLO. The calculation includes the subsequent decay of the Higgs boson into four leptons, allowing for the full reconstruction of the final-state kinematics. In anticipation of improved LHC measurements based on the full Run II dataset, we present a study for single- and double-differential cross sections within the fiducial volume as defined in prior ATLAS analyses. Higher-order corrections are found to have a sizeable impact on both normalisation and shape of differential cross sections.
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