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The cross-section for the production of a single top quark in associationwith a $W$ boson in proton--proton collisions at $\sqrt{s}= 8$ TeV 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 $Wt$signal is separated from the backgrounds using boosted decision trees, each ofwhich combines a number of discriminating variables into one classifier.Production of $Wt$ events is observed with a significance of $7.7 \sigma$. Thecross-section is extracted in a profile likelihood fit to the classifier outputdistributions. The $Wt$ cross-section, inclusive of decay modes, is measured tobe $23.0 \pm 1.3$(stat.)$^{+3.2}_{-3.5}$(syst.)$\pm 1.1$(lumi.) pb. Themeasured cross-section is used to extract a value for the CKM matrix element$|V_{tb}|$ of $1.01 \pm 0.10$ and a lower limit of 0.80 at the 95\% confidencelevel. The cross-section for the production of a top quark and a $W$ boson isalso measured in a fiducial acceptance requiring two leptons with$p_{\textrm{T}}>25$ GeV and $|\eta|<2.5$, one jet with $p_{\textrm{T}}>20$ GeVand $|\eta|<2.5$, and $E_{\textrm{T}}^{\textrm{miss}}>20$ GeV, including both$Wt$ and top-quark pair events as signal. The measured value of the fiducialcross-section is $0.85 \pm 0.01$(stat.)$^{+0.06}_{-0.07}$(syst.)$\pm0.03$(lumi.) pb.

Measurement of the production cross-section of a single top quark in association with a $W$ boson at 8 TeV with the ATLAS experiment