Combination of searches for singly produced vector-like top quarks in pp collisions at $\sqrt{s} = 13$ TeV with the ATLAS detector

A combination of searches for the single production of vector-like top quarks ($T$) is presented. These analyses are based on proton$-$proton collisions at $\sqrt{s}=13$ TeV recorded in 2015$-$2018 with the ATLAS detector at the Large Hadron Collider, corresponding to an integrated luminosity of 139 fb$^{-1}$. The $T$-quark decay modes considered in this combination are into a top quark and either a Standard Model Higgs boson or a $Z$ boson ($T \to Ht$ and $T \to Zt$). The individual searches used in the combination are differentiated by the number of leptons ($e$, $\mu$) in the final state. The observed data are found to be in good agreement with the Standard Model background prediction. Interpretations are provided for a range of masses and couplings of the vector-like top quark for benchmark models and generalized representations in terms of 95% confidence level limits. For a benchmark signal prediction of a vector-like top quark SU2 singlet with electroweak coupling, $\kappa$, of 0.5, masses below 2.1 TeV are excluded, resulting in the most restrictive limits to date.