Anomalous couplings in Higgs boson pair production at approximate NNLO QCD

We combine NLO predictions with full top quark mass dependence with approximate NNLO predictions for Higgs boson pair production in gluon fusion, including the possibility to vary coupling parameters within a non-linear Effective Field Theory framework containing five anomalous couplings for this process. We study the impact of the anomalous couplings on various observables, and present Higgs pair invariant mass distributions at seven benchmark points characterising different $m_{hh}$ shape types. We also provide numerical coefficients for the approximate NNLO cross section as a function of the anomalous couplings at $\sqrt{s}=14$ TeV.