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No significant excess over the expected standard model background is observed in the $\\ell\\nu$qq and 2$\\ell$2$\\nu$ final states of the W$^+$W$^-$ boson pair. Limits are set on dark matter production in the context of a simplified dark Higgs model, with a dark Higgs boson mass above the W$^+$W$^-$ mass threshold. The dark matter phase space is probed in the mass range 100-300 GeV, extending the scope of previous searches. Current exclusion limits are improved in the range of dark Higgs masses from 160 to 250 GeV, for a dark matter mass of 200 GeV.","hasPart":[{"@id":"https://doi.org/10.17182/hepdata.139719.v1/t1","@type":"Dataset","description":"Leading lepton $p_T$ pre-fit distribution for selected events in SR1 of the di-leptonic channel for the full dataset. 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