  The first computation of Higgs production in association with three jets at
NLO in QCD has recently been performed using the effective theory, where the
top quark is treated as an infinitely heavy particle and integrated out. This
approach is restricted to the regions in phase space where the typical scales
are not larger than the top quark mass. Here we investigate this statement at a
quantitative level by calculating the leading-order contributions to the
production of a Standard Model Higgs boson in association with up to three jets
taking full top-quark and bottom-quark mass dependence into account. We find
that the transverse momentum of the hardest particle or jet plays a key role in
the breakdown of the effective theory predictions, and that discrepancies can
easily reach an order of magnitude for transverse momenta of about 1 TeV. The
impact of bottom-quark loops are found to be visible in the small transverse
momentum region, leading to corrections of up to 5 percent. We further study
the impact of mass corrections when VBF selection cuts are applied and when the
center-of-mass energy is increased to 100 TeV.
