Search for Higgs boson pair production in association with top-quark pairs using 196 fb${}^{-1}$ of proton-proton collision data at $\sqrt{s}=$ 13 and 13.6 TeV with the ATLAS detector

This paper presents the first search for non-resonant Higgs boson pair production in association with a top-quark pair ($t\bar{t}HH$) 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 $\sqrt{s}=13$ TeV and 56 fb${}^{-1}$ at 13.6 TeV. The search targets three distinct final states expected from $t\bar{t}HH$ 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 $t\bar{t}HH$ production cross-section, relative to its Standard Model prediction, is measured to be ${\mu }_{t\bar{t}HH}=-3_{-12}^{+11}$. This result corresponds to a 95$\mathrm{\%}$ confidence-level upper limit of 20 times the Standard Model prediction for the $t\bar{t}HH$ production cross-section, with an expected limit of 21. The Higgs effective field theory Wilson coefficient $c_{t\bar{t}HH}$ is also constrained at the same confidence level to the range of $-3.9<c_{t\bar{t}HH}<3.3$, compared with the expected range of $-4.0<c_{t\bar{t}HH}<3.5$.