We present the calculation of the dominant next to leading order QCD corrections to Higgs boson production in association with three jets via vector boson fusion in the form of a NLO parton-level Monte Carlo program. QCD corrections to integrated cross sections are modest, while the shapes of some kinematical distributions change appreciably at NLO. Scale uncertainties are shown to be reduced at NLO for the total cross section and for distributions. We consider a central jet veto at the LHC and analyze the veto probability for typical vector boson fusion cuts. Scale uncertainties of the veto probability are sufficiently small at NLO for precise Higgs coupling measurements at the LHC.
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