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

A search for a new heavy scalar or pseudo-scalar Higgs boson ($H/A$) produced in association with a pair of top quarks, with the Higgs boson decaying into a pair of top quarks ($H/A \rightarrow t\bar t$) is reported. The search targets a final state with two leptons with the same-sign electric charge or at least three leptons. The analysed dataset corresponds to an integrated luminosity of 139 fb$^{-1}$~of proton-proton collisions data collected at a centre-of-mass energy of 13 TeV with the ATLAS detector at the LHC. A multivariate classifier is used to separate the signal from the background. No significant excess of events over the Standard Model expectation is observed. The results are interpreted in the context of the two-Higgs-doublet model of type~II. The observed (expected) upper limits at 95% CL on the $t\bar tH/A$ cross-section times the branching ratio of $H/A \rightarrow t\bar t$ range between 14 (10) fb and 6 (5) fb for a heavy Higgs boson mass between 400 and 1000 GeV, respectively. Assuming the presence of only one particle, either the scalar $H$ or the pseudo-scalar $A$, the values of $\tan\beta$ below 1.2 and 0.5 are excluded for the studied mass range. This exclusion range increases up to $\tan\beta$ between 1.6 and 0.6 when both particles are present.