The production of a Higgs boson in association with jets suffers from
large higher order corrections, which are known at NNLO for a single
accompanying jet and at NLO for up to three jets. These results are
computed 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 in detail the validity range of such effective theory
predictions. In this talk I will compare them to results obtained in the
full theory, considering top and bottom quark mass effects, for up to
three extra jets.