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v3.3.2-pre
It is well known that Higgs boson productions suffers from large higher order corrections. This is true also when it is accompanied by one or more jets. The most precise results rely on computations in an effective theory where the heavy quark loops, mediating the coupling between the Higgs boson and the gluons, are integrated out. As the LHC is delivering more and more precise data it is important to understand the validity range of the effective theory predictions and to improve the accuracy of the results with finite mass corrections. These allow to disentangle the Standard Model contribution from potential New Physics effects appearing in boosted regimes. In this talk I will present detailed comparisons between effective theory results and predictions obtained in the full theory, focussing in particular on the newly available NLO QCD corrections to H+1j production with full top-quark mass dependence.