Search for heavy resonances in four-top-quark final states in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector

A search for associated production of a heavy $Z'$ boson with a top-antitop-quark pair $(t\bar{t}Z')$, and decaying into a $t\bar{t}$ pair is presented. The search uses $pp$ collision data at $\sqrt{s}= 13$ TeV recorded by the ATLAS detector at the Large Hadron Collider during the years 2015--2018, and corresponding to an integrated luminosity of 139 fb$^{-1}$. The two top quarks from the resonance decay are reconstructed using jets clustered with a large radius parameter of $R=1$. The invariant mass spectrum of the two top quark candidates is used to search for a resonance signal in the range of 1.0 TeV to 3.2 TeV. The selected events contain exactly one electron or muon in association with multiple jets. They are categorized into signal-enriched or signal-depleted regions according to the multiplicity of jets and how likely these contain $b$-hadrons. The presence of a signal is examined in the signal-enriched regions using an approach with minimal model dependence followed by a model-dependent interpretation. No significant excess is observed over the background expectation. Upper limits on the production cross section times branching ratio at 95% confidence level are provided as a function of $Z^\prime$ mass between 1.0 TeV and 3.0 TeV, based on a simplified $Z^\prime$ production model. The observed limits range from 65 fb to 12 fb for $Z^\prime$ masses between 1.0 TeV and 3.0 TeV, respectively.