NLO QCD+EW predictions for $2\ell2\nu$ diboson signatures at the LHC

We present next-to-leading order (NLO) calculations including QCD and electroweak (EW) corrections for 2ℓ2ν diboson signatures with two opposite-charge leptons and two neutrinos. Specifically, we study the processes $ pp\to {e}^{+}{\mu}^{-}{\nu}_e{\overline{\nu}}_{\mu } $ and $ pp\to {e}^{+}{e}^{-}\nu \overline{\nu} $ , including all relevant off-shell diboson channels, W$^{+}$ W$^{−}$, ZZ, γZ, as well as non-resonant contributions. Photon-induced processes are computed at NLO EW, and we discuss subtle differences related to the definition and the renormalisation of the coupling α for processes with initial- and final-state photons. All calculations are performed within the automated Munich/Sherpa+OpenLoops frameworks, and we provide numerical predictions for the LHC at 13 TeV. The behaviour of the corrections is investigated with emphasis on the high-energy regime, where NLO EW effects can amount to tens of percent due to large Sudakov logarithms. The interplay between W W and ZZ contributions to the same-flavour channel, $ pp\to {e}^{+}{e}^{-}\nu \overline{\nu} $ , is discussed in detail, and a quantitative analysis of photon-induced contributions is presented. Finally, we consider approximations that account for all sources of large logarithms, at high and low energy, by combining virtual EW corrections with a YFS soft-photon resummation or a QED parton shower.