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A search for new charged massive gauge bosons, called W′W′, is performed with the ATLAS detector at the LHC, in proton–proton collisions at a centre-of-mass energy of \(\sqrt {s}\)=8 TeV, using a dataset corresponding to an integrated luminosity of 20.3 fb\(^{−1}\). This analysis searches for W′W′ bosons in the \(W′→t\overline{b}\) decay channel in final states with electrons or muons, using a multivariate method based on boosted decision trees. The search covers masses between 0.5 and 3.0 TeV, for right-handed or left-handed W′W′ bosons. No significant deviation from the Standard Model expectation is observed and limits are set on the \(W′→t\overline{b}\) cross-section times branching ratio and on the W′W′-boson effective couplings as a function of the W′W′-boson mass using the CL\(_s\) procedure. For a left-handed (right-handed) W′W′ boson, masses below 1.70 (1.92) TeV are excluded at 95% confidence level.