Next-to-leading order electroweak corrections to off-shell WWW production at the LHC

Triboson processes allow for a measurement of the triple and quartic couplings of the Standard Model gauge bosons, which can be used to constrain anomalous gauge couplings. In this paper we calculate the next-to-leading order electroweak corrections to fully off-shell $W^{-}{W}^{+}{W}^{+}$ production, namely the production of a ${\ell }_1^{-}{\ell }_2^{+}{\ell }_3^{+}{\overline{\nu }}_{{\ell }_1}{\nu }_{{\ell }_2}{\nu }_{{\ell }_3}$ final state with (${\ell }_i=e,\mu$), including all triple, double, single and non resonant topologies and interferences of diagrams with all different vector boson ($W,Z,\gamma$) intermediate states. We find large cancellations of the electroweak correction to the $q\overline{q}$-induced channel, which includes the exchange of virtual electroweak gauge bosons, and photon-induced jet radiation processes. This accidental compensation is found to be strongly phase space and observable dependent. The resulting corrections in a suitably defined fiducial region thus amount to $-2.0\%$, but rise rapidly for other observables.