# $W^\pm Z$ production at the LHC: fiducial cross sections and distributions in NNLO QCD

## TL;DR

This paper presents the first fully differential NNLO QCD calculation for W±Z production at the LHC, including leptonic decays and realistic experimental cuts, improving theoretical precision and agreement with data.

## Contribution

It provides the first differential NNLO QCD predictions for W±Z production including leptonic decays and experimental cuts, enhancing precision for LHC analyses.

## Key findings

- NNLO corrections increase NLO results by about 10%.
- Improved agreement with experimental data.
- NNLO effects can reach 20% in high-pT regions.

## Abstract

We report on the first fully differential calculation for $W^\pm Z$ production in hadron collisions up to next-to-next-to-leading order (NNLO) in QCD perturbation theory. Leptonic decays of the $W$ and $Z$ bosons are consistently taken into account, i.e. we include all resonant and non-resonant diagrams that contribute to the process $pp\to \ell^{'\pm} \nu_{\ell^{'}} \ell^+\ell^-+X$ both in the same-flavour ($\ell'=\ell$) and the different-flavour ($\ell'\neq \ell$) channel. Fiducial cross sections and distributions are presented in the presence of standard selection cuts applied in the experimental $W^\pm Z$ analyses by ATLAS and CMS at centre-of-mass energies of 8 and 13\,TeV. As previously shown for the inclusive cross section, NNLO corrections increase the NLO result by about $10\%$, thereby leading to an improved agreement with experimental data. The importance of NNLO accurate predictions is also shown in the case of new-physics scenarios, where, especially in high-$p_T$ categories, their impact can reach ${\cal O}(20\%)$. The availability of differential NNLO predictions will play a crucial role in the rich physics programme that is based on precision studies of $W^\pm Z$ signatures at the LHC.