Search for $t\bar{t}H/A \rightarrow t\bar{t}t\bar{t}$ production in proton-proton collisions at $\sqrt{s}=13$ TeV with the ATLAS detector

A search is presented for a heavy scalar ($H$) or pseudo-scalar ($A$) predicted by the two-Higgs-doublet models, where the $H/A$ is produced in association with a top-quark pair ($t\bar{t}H/A$), and with the $H/A$ decaying into a $t\bar{t}$ pair. Events are selected requiring exactly one or two opposite-charge electrons or muons. Data-driven corrections are applied to improve the modelling of the $t\bar{t}$+jets background in the regime with high jet and $b$-jet multiplicities. These include a novel multi-dimensional kinematic reweighting based on a neural network trained using data and simulations. An $H/A$-mass parameterised graph neural network is trained to optimise the signal-to-background discrimination. In combination with the previous search performed by the ATLAS Collaboration in the multilepton final state, the observed upper limits on the $t\bar{t}H/A \rightarrow t\bar{t}t\bar{t}$ production cross-section at 95% confidence level range between 14 fb and 5.0 fb for an $H/A$ with mass between 400 GeV and 1000 GeV, respectively. Assuming that both the $H$ and $A$ contribute to the $t\bar{t}t\bar{t}$ cross-section, $\tan\beta$ values below 1.7 or 0.7 are excluded for a mass of 400 GeV or 1000 GeV, respectively. The results are also used to constrain a model predicting the pair production of a colour-octet scalar, with the scalar decaying into a $t\bar{t}$ pair.