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Top-quark mass effects in double and triple Higgs production in gluon-gluon fusion at NLO

The observation of double and triple scalar boson production at hadron colliders could provide key information on the Higgs self couplings and the potential. As for single Higgs production the largest rates for multiple Higgs production come from gluon-gluon fusion processes mediated by a top-quark loop. However, at variance with single Higgs production, top-quark mass and width effects from the loops cannot be neglected. Computations including the exact top-quark mass dependence are only available at the leading order, and currently predictions at higher orders are obtained by means of approximations based on the Higgs-gluon effective field theory (HEFT). In this work we present a reweighting technique that, starting from events obtained via the MC@NLO method in the HEFT, allows to exactly include the top-quark mass and width effects coming from one- and two-loop amplitudes. We describe our approach and apply it to double Higgs production at NLO in QCD, computing the needed one-loop amplitudes and using approximations for the unknown two-loop ones. The results are compared to other approaches used in the literature, arguing that they provide more accurate predictions for distributions and for total rates as well. As a novel application of our procedure we present predictions at NLO in QCD for triple Higgs production at hadron colliders.