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An important ingredient for the calculation of Higgs boson properties in theinfinite top quark mass limit is the knowledge of the effective couplingbetween the Higgs bosons and gluons, i.e. the Wilson coefficients $C_H$ and$C_{HH}$ for one and two Higgs bosons, respectively. In this work we calculatefor the first time $C_{HH}$ to four loops in a direct, diagrammatic way,discussing in detail all issues arising due to the renormalization of operatorproducts. Furthermore, we also calculate the Wilson coefficient $C_H$ for thecoupling of a single Higgs boson to gluons as well as all four loop decouplingrelations in QCD with general SU$(N_c)$ colour factors. The latter are relatedto $C_H$ and $C_{HH}$ via low-energy theorems.

Wilson coefficients for Higgs boson production and decoupling relations to $\mathcal{O}\left(\alpha_s^4\right)$