Inclusive $W^{\pm}$ and $Z^{0}$ cross sections at next-to-next-to leading order QCD for the ATLAS experiment

This note presents the evaluation of the cross sections for the production of single electroweak vector bosons ($W$, $Z/\gamma^{*}$) in proton--proton collisions using state-of-the-art calculations for use in the ATLAS experiment at the Large Hadron Collider. The calculations are performed with a focus on the LHC Run 3 centre-of-mass energy of $\sqrt{s} = 13.6 \, \text{TeV}$ and in the phase space of the most common ATLAS Monte Carlo samples. Calculations for the centre-of-mass energies of $5.02$, $7$, $8$, $13$, and $14\, \text{TeV}$ are also provided. The calculations are performed up to next-to-next-to leading order in the strong coupling and up to next-to-leading order in the electroweak coupling. Uncertainties on the predictions are evaluated from the variation of perturbative scales and from the parton density function sets used. Cross sections for different values of the strong coupling and with the effects of photon induced parton density functions included are also provided. The results from this note will be used for setting the normalisation of the Monte Carlo simulations for single electroweak production in ATLAS analyses.