A search for singly produced vector-like Q quarks, where Q can be either a T quark with charge $+2/3$ or a Y quark with charge $-4/3$ , is performed in proton–proton collisions recorded with the ATLAS detector at the LHC. The dataset corresponds to an integrated luminosity of 20.3 fb$^{-1}$ and was produced with a centre-of-mass energy of $\sqrt{s}=8$ TeV. This analysis targets $Q \rightarrow Wb$ decays where the W boson decays leptonically. A veto on massive large-radius jets is used to reject the dominant $t\bar{t}$ background. The reconstructed Q-candidate mass, ranging from 0.4 to 1.2 TeV, is used in the search to discriminate signal from background processes. No significant deviation from the Standard Model expectation is observed, and limits are set on the $Q \rightarrow Wb$ cross-section times branching ratio. The results are also interpreted as limits on the QWb coupling and the mixing with the Standard Model sector for a singlet T quark or a Y quark from a doublet. T quarks with masses below 0.95 TeV are excluded at 95 % confidence level, assuming a unit coupling and a BR $(T\rightarrow Wb) = 0.5$ , whereas the expected limit is 1.10
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