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This paper presents a search for dark matter, $\chi$, using events with asingle top quark and an energetic $W$ boson. The analysis is based onproton-proton collision data collected with the ATLAS experiment at $\sqrt{s}=$13 TeV during LHC Run 2 (2015-2018), corresponding to an integrated luminosityof 139 fb$^{-1}$. The search considers final states with zero or one chargedlepton (electron or muon), at least one $b$-jet and large missing transversemomentum. In addition, a result from a previous search consideringtwo-charged-lepton final states is included in the interpretation of theresults. The data are found to be in good agreement with the Standard Modelpredictions and the results are interpreted in terms of 95% confidence-levelexclusion limits in the context of a class of dark matter models involving anextended two-Higgs-doublet sector together with a pseudoscalar mediatorparticle. The search is particularly sensitive to on-shell production of thecharged Higgs boson state, $H^{\pm}$, arising from the two-Higgs-doubletmixing, and its semi-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 atan$\beta$ value of 1. For masses of $a$ of 150 (250) GeV, tan$\beta$ values upto 2 are excluded for $H^{\pm}$ masses between 200 (400) GeV and 1.5 TeV.Signals with tan$\beta$ values between 20 and 30 are excluded for $H^{\pm}$masses between 500 and 800 GeV.

european physical journal. c, particles and fields

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