Precision calculations for electroweak multi-boson processes

Abstract: We review the salient features of next-to-leading-order QCD and electroweak corrections to the scattering of two and the production of three weak gauge bosons at the Large Hadron Collider. Results for the tower of $O(α_s^mα^n)$ corrections are shown for the exemplary processes of like-sign WW scattering and triple-W production, emphasizing the large impact of purely electroweak corrections which generically grow to $\sim-16\%$ and $\sim-7\%$ for these process types, respectively, even for integrated cross sections. Moreover, we discuss the possibility to reproduce the results of full off-shell calculations by the "vector-boson scattering approximation", "leading-pole approximations", and the "effective vector-boson approximation".