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

## TL;DR

This paper provides detailed NLO QCD and electroweak predictions for $2 ext{l}2
u$ diboson signatures at the LHC, including off-shell effects, photon-induced processes, and high-energy corrections, with implications for precision measurements.

## Contribution

It introduces comprehensive NLO calculations for diboson signatures, incorporating off-shell, non-resonant, and photon-induced effects, and discusses advanced resummation techniques for large logarithms.

## Key findings

- NLO EW effects can reach tens of percent at high energies.
- Photon-induced processes significantly impact the predictions.
- Resummation methods improve accuracy for large logarithmic corrections.

## Abstract

We present next-to-leading order (NLO) calculations including QCD and electroweak (EW) corrections for $2\ell2\nu$ diboson signatures with two opposite-charge leptons and two neutrinos. Specifically, we study the processes $pp\to e^+ \mu^- \nu_{e}\bar\nu_{\mu}$ and $pp\to e^+ e^-\nu\bar\nu$, including all relevant off-shell diboson channels, $W^+W^-$, $ZZ$, $\gamma Z$, 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 $\alpha$ 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 $WW$ and $ZZ$ contributions to the same-flavour channel, $pp\to e^+ e^-\nu\bar\nu$, 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.