Search for dark matter produced in association with a single top quark and an energetic $W$ boson in $\sqrt{s}=13$ TeV ($pp$) collisions with the ATLAS detector

This paper presents a search for dark matter, $\chi$, using events with a single top quark and a highly energetic $W$ boson. The analysis is based on proton-proton collision data collected with the ATLAS experiment at $\sqrt{s} = 13$ TeV during LHC Run 2 (2015-2018), corresponding to an integrated luminosity of 139 fb$^{-1}$. The search considers final states with zero or one charged lepton (electron or muon), at least one $b$-jet and large missing transverse momentum. In addition, a result defined in a previous search considering two charged lepton final states is included in the interpretation of results. The data are found to be in good agreement with the Standard Model predictions and the results are interpreted in terms of 95% confidence level exclusion limits in the context of a class of dark matter models involving an extended two-Higgs-doublet sector together with a pseudoscalar mediator particle. The search is particularly sensitive to on-shell production of the charged Higgs boson state, $H^{\pm}$, arising from the two-Higgs-doublet mixing and its invisible decays via the mediator particle, $a$: $H^{\pm} \rightarrow W^\pm a (\rightarrow \chi\chi)$. Signal models with $H^{\pm}$ masses up to 1.5 TeV and $a$ masses up to 350 GeV are excluded assuming a tan$\beta$ equal to 1. Masses of $a$ of 150 (250) GeV, tan$\beta$ values up to 2 are excluded for $H^{\pm}$ masses between 200 (400) GeV and 1.5 GeV. Signals with tan$\beta$ values between 20 and 30 are excluded for $H^{\pm}$ masses between 500 and 800 GeV.