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In this talk we discuss recent computations of the top quark mass dependenceof QCD amplitudes describing Higgs boson production in gluon fusion. We computeterms in the expansion for a large top quark mass, which reduces the Feynmandiagrams to products of massless integrals and massive tadpole integrals whichcontain the top mass dependence. In particular we discuss the real and virtualcorrections to double Higgs production at NNLO, and the virtual corrections tosingle Higgs production at N3LO.

Top quark mass corrections to single and double Higgs boson production in gluon fusion