Search for production of vector-like top quark pairs and of four top quarks in the lepton-plus-jets final state in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector

A search for pair production of vector-like top quarks ($T$) with significant branching ratio to a Higgs boson and a top quark, $T\bar{T} \to Ht$+X, is presented. The same analysis is also used to search for four-top-quark production, both within the Standard Model and in several new physics scenarios. The analysis is based on $pp$ collisions at $\sqrt{s}=13$ TeV recorded in 2015 with the ATLAS detector at the CERN Large Hadron Collider. The dataset corresponds to an integrated luminosity of 3.2 fb$^{-1}$. Data are analysed in the lepton-plus-jets final state, characterised by an isolated electron or muon with high transverse momentum, large missing transverse momentum and multiple jets. The search exploits the high multiplicity of $b$-jets, the high scalar sum of transverse momenta of all final state objects, and the presence of boosted, hadronically-decaying resonances reconstructed as large-radius jets, characteristic of signal events. No significant excess of events above the Standard Model expectation is observed, and 95% CL lower limits are derived on the mass of the vector-like $T$ quark under several branching ratio hypotheses assuming contributions only from $T \to Wb$, $Zt$, $Ht$. The 95% CL observed lower limits on the $T$ quark mass range between $700$ GeV and $900$ GeV for all possible values of the branching ratios into the three decay modes. Under the assumption of BR$(T \to Ht)=1$, an observed (expected) 95% CL limit of $m_{T}>900\,(980)$ GeV is obtained. The observed (expected) 95% CL limits for a weak-isospin doublet and singlet are $m_{T}>800\,(900)$ GeV and $m_{T}>750\,(780)$ GeV respectively. Additionally, upper bounds on the four-top-quark production cross section are set in several scenarios, significantly extending the reach of previous searches.