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We present a new calculation of next-to-leading-order corrections of thestrong and electroweak interactions to like-sign W-boson scattering at theLarge Hadron Collider, implemented in the Monte Carlo integrator Bonsay. Thecalculation includes leptonic decays of the $\mathrm{W}$ bosons. It comprisesthe whole tower of next-to-leading-order contributions to the cross section,which scale like $\alpha_\mathrm{s}^3\alpha^4$, $\alpha_\mathrm{s}^2\alpha^5$,$\alpha_\mathrm{s}\alpha^6$, and $\alpha^7$ in the strong and electroweakcouplings $\alpha_\mathrm{s}$ and $\alpha$. We present a detailed survey ofnumerical results confirming the occurrence of large pure electroweakcorrections of the order of $\sim-12\%$ for integrated cross sections and evenlarger corrections in high-energy tails of distributions. The electroweakcorrections account for the major part of the complete next-to-leading-ordercorrection, which amounts to $15{-}20\%$ in size, depending on the details ofthe event selection chosen for analysing vector-boson-scattering. Moreover, wecompare the full next-to-leading-order corrections to approximate results basedon the neglect of contributions that are not enhanced by the vector-bosonscattering kinematics (VBS approximation) and on resonance expansions for the$\mathrm{W}$-boson decays (double-pole approximation); the quality of thisapproximation is good within $\sim 1.5\%$ for integrated cross sections and thedominating parts of the differential distributions. Finally, for theleading-order predictions, we construct different versions of effectivevector-boson approximations, which are based on cross-section contributionsthat are enhanced by collinear emission of $\mathrm{W}$ bosons off theinitial-state (anti)quarks; in line with previous findings in the literature,it turns out that the approximative quality is rather limited for applicationsat the LHC.

Like-Sign W-Boson Scattering at the LHC -- Approximations and Full Next-to-Leading-Order Predictions