We present the full next-to-leading-order electroweak and QCD corrections to vector-boson scattering into a pair of off-shell opposite-sign W bosons decaying into leptons of different flavour at the LHC. We include full leading-order predictions for the irreducible background. Explicitly, we investigate the process pp → e+νeμ−ν¯\documentclass[12pt]{minimal}
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\begin{document}$$ \overline{\nu} $$\end{document}μjj + X at leading orders O\documentclass[12pt]{minimal}
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\begin{document}$$ \mathcal{O} $$\end{document}(α6), O\documentclass[12pt]{minimal}
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\begin{document}$$ \mathcal{O} $$\end{document}(αsα5), O\documentclass[12pt]{minimal}
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\begin{document}$$ {\alpha}_{\mathrm{s}}^2 $$\end{document}α4), supplemented by the loop-induced O\documentclass[12pt]{minimal}
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\begin{document}$$ {\alpha}_{\mathrm{s}}^4 $$\end{document}α4) contribution, and at next-to-leading orders O\documentclass[12pt]{minimal}
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\begin{document}$$ \mathcal{O} $$\end{document}(α7)and O\documentclass[12pt]{minimal}
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\begin{document}$$ \mathcal{O} $$\end{document}(αsα6) in two setups providing fiducial cross sections as well as differential distributions. We take full account of photon-induced next-to-leading-order contributions, which prove to be non negligible. With −11.4% and −6.7% in the two setups, the electroweak corrections are smaller than for other vector-boson-scattering processes. This can be traced back to the presence of the Higgs-boson resonance in the fiducial phase space, whose effects we analyse within an additional unphysical, but manifestly gauge-invariant setup. The QCD corrections amount to −5.1% and −21.6% in the two setups. The large size of the latter correction, compared to other vector-boson scattering processes, is explained by a very restrictive definition of its fiducial phase space.
