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Effects from a finite top quark mass on the H+n-jet cross section throughgluon fusion are studied for $n=0/n\ge 1$ at NNLO/NLO QCD. For this purpose,sub-leading terms in $1/m_t$ are calculated. We show that the asymptoticexpansion of the jet-vetoed cross section at NNLO is very well behaved and thatthe heavy-top approximation is valid at the five permille level up to jet-vetocuts of 300 GeV. For the inclusive Higgs+jet rate, we introduce a matchingprocedure that allows for a reliable prediction of the top-mass effects usingthe expansion in $1/m_t$. The quality of the effective field theory to evaluatedifferential K-factors for the distribution of the hardest jet is found to bebetter than 1-2% as long as the transverse momentum of the jet is integratedout or remains below about 150 GeV.

Finite top-mass effects in gluon-induced Higgs production with a jet-veto at NNLO