Addendum to: Constraints on the quartic Higgs self-coupling from double-Higgs production at future hadron colliders

Abstract: We study inclusive double-Higgs boson production at the LHC and at the HL-LHC including variations of the trilinear and of the quartic Higgs boson self-couplings at next-to-leading order (NLO) in QCD with full top quark mass dependence. Our results include the two-loop contributions to the $gg \rightarrow HH$ amplitudes that involve a modified $h_4$ vertex calculated in arXiv:1810.04665. We present results at 13, 13.6 and 14 TeV centre-of-mass energies. The implementation of the calculation is made publicly available in the POWHEG-BOX-V2 Monte Carlo framework.