Matching coefficient for Higgs boson pair production in gluon fusion at NNLO

The cross section for Higgs boson pair production is of great interest since it gives access to the Higgs boson self interaction and the Higgs potential of the SM. It receives large radiative corrections, such that NLO corrections are essential and NNLO corrections are not negligible. For a consistent description of this process at NNLO in the heavy top quark effective theory, the matching coefficient describing the gluon-gluon-Higgs-Higgs (ggHH) interaction is needed to three-loop accuracy. We compute the ggHH matching coefficient and find that it differs from the gluon-gluon-Higgs (ggH) matching coefficient at NNLO, whereas both matching coefficients coincide up to NLO. We discuss the validity of the heavy top approximation and the effect of the ggHH matching coefficient on Higgs boson pair production at the LHC.