Next-to-leading-order electroweak corrections to the production of three charged leptons plus missing energy at the LHC

The production of a neutral and a charged vector boson with subsequent decays into three charged leptons and a neutrino is a very important process for precision tests of the Standard Model of elementary particles and in searches for anomalous triple-gauge-boson couplings. In this article, the first computation of next-to-leading-order electroweak corrections to the production of the four-lepton final states $\mu^+\mu^- e^+ \nu_e$, $\mu^+\mu^- e^- \bar\nu_e$, $\mu^+\mu^- \mu^+\nu_\mu$, and $\mu^+\mu^- \mu^- \bar\nu_\mu$ at the Large Hadron Collider is presented. We use the complete matrix elements at leading and next-to-leading order, including all off-shell effects of intermediate massive vector bosons and virtual photons. The relative electroweak corrections to the fiducial cross sections from quark-induced partonic processes vary between $-3\%$ and $-6\%$, depending significantly on the event selection. At the level of differential distributions, we observe large negative corrections of up to $-30\%$ in the high-energy tails of distributions originating from electroweak Sudakov logarithms. Photon-induced contributions at next-to-leading order raise the leading-order fiducial cross section by $+2\%$. Interference effects in final states with equal-flavour leptons are at the permille level for the fiducial cross section, but can lead to sizeable effects in off-shell sensitive phase-space regions.