  Recently a lot of progress has been made towards a full classification of new
physics effects in Higgs observables by means of effective dimension six
operators. Specifically, Higgs production in association with a high transverse
momentum jet has been suggested as a way to discriminate between operators that
modify the Higgs-top coupling and operators that induce an effective
Higgs-gluon coupling---a distinction that is hard to achieve with signal
strength measurements alone. With this article we would like to draw attention
to another source of new physics in Higgs+jet observables: the triple gluon
operator $O_{3g}$ (consisting of three factors of the gluon field strength
tensor). We compute the distortions of kinematic distributions in Higgs+jet
production at a 14 TeV LHC due to $O_{3g}$ and compare them with the
distortions due to dimension six operators involving the Higgs doublet. We find
that the transverse momentum, the jet rapidity and the difference between the
Higgs and jet rapidity are well suited to distinguish between the contributions
from $O_{3g}$ and those from other operators, and that the size of the
distortions are similar if the Wilson coefficients are of the same order as the
expected bounds from other observables. We conclude that a full analysis of new
physics in Higgs+jet observables must take the contributions from $O_{3g}$ into
account.
