This paper presents the first search for non-resonant Higgs boson pair production in association with a top-quark pair (ttHH) using proton-proton collision data collected with the ATLAS detector at the Large Hadron Collider. The data sample corresponds to an integrated luminosity of 196 fb^-1, comprising 140 fb^-1 at a centre-of-mass energy of s=13 TeV and 56 fb^-1 at 13. 6 TeV. The search targets three distinct final states expected from ttHH decays: (i) one lepton (electron or muon) with at least five b-quarks, (ii) at least two b-quarks accompanied by two leptons with the same electric charges or multiple leptons, and (iii) at least three b-quarks with two photons. The ttHH production cross-section, relative to its Standard Model prediction, is measured to be μₓₓ₇₇=-3^+11-₁₂. This result corresponds to a 95\% confidence-level upper limit of 20 times the Standard Model prediction for the ttHH production cross-section, with an expected limit of 21. The Higgs effective field theory Wilson coefficient cₓₓ₇₇ is also constrained at the same confidence level to the range of -3. 9
Aad et al. (Thu,) studied this question.