The cross-section for the production of a single top quark in association with a W boson in proton-proton collisions at $ \sqrt{s}=8\mathrm{T}\mathrm{e}\mathrm{V} $ is measured. The dataset corresponds to an integrated luminosity of 20.3 fb$^{−1}$, collected by the ATLAS detector in 2012 at the Large Hadron Collider at CERN. Events containing two leptons and one central b-jet are selected. The W t signal is separated from the backgrounds using boosted decision trees, each of which combines a number of discriminating variables into one classifier. Production of W t events is observed with a significance of 7.7σ. The cross-section is extracted in a profile likelihood fit to the classifier output distributions. The W t cross-section, inclusive of decay modes, is measured to be 23.0 ± 1.3(stat.)$_{− 3.5}^{+ 3.2}$ (syst.)±1.1(lumi.) pb. The measured cross-section is used to extract a value for the CKM matrix element |V$_{tb}$ | of 1.01 ± 0.10 and a lower limit of 0.80 at the 95% confidence level. The cross-section for the production of a top quark and a W boson is also measured in a fiducial acceptance requiring two leptons with p$_{T}$ > 25 GeV and |η| < 2.5, one jet with p$_{T}$ > 20 GeV and |η| < 2.5, and E$_{T}^{miss}$ > 20 GeV, including both W t and top-quark pair events as signal. The measured value of the fiducial cross-section is 0.85 ± 0.01(stat.)$_{− 0.07}^{+ 0.07}$ (syst.)±0.03(lumi.)
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