Luminosity Determination using $Z\rightarrow \ell \ell$ events at $\sqrt{s} = 13$ TeV with the ATLAS detector

During Run 2, the maximum instantaneous luminosity delivered by the Large Hadron Collider to the ATLAS and CMS experiments reached $19 \times10^{33}$ cm$^{-2}$ s$^{-1}$ in $pp$ collisions at $\sqrt{s}=$13~TeV. This permitted monitoring of the luminosity, with a time granularity of about 60 s, using the counts of reconstructed $Z\rightarrow \ell \ell$ events, where two muons or electrons with $p_T^{\ell}>27$~GeV, $|\eta^{\ell}|<2.4$ and $66<m_{\ell\ell}<116$~GeV are selected. The $Z$-counting rate is corrected using trigger and reconstruction efficiencies determined from data, as well as a Monte Carlo correction for residual detector effects, calculated as a function of the mean number of inelastic $pp$ interactions per crossing. When integrated over 20 minutes, the $Z$-counting rate has a statistical precision of approximately 2 to 4\%. This note describes how the counting of $Z\rightarrow \ell \ell$ bosons can be used as a relative luminometer, and quantifies the internal consistency of the method by comparing the luminosities obtained in the $Z \rightarrow e^+e^-$ and $Z \rightarrow \mu^+\mu^-$ channels. The $Z$-counting rates are further compared to the baseline ATLAS luminosity measured by the LUCID detector. The excellent stability of these ratios with respect to time and the pileup-parameter $<\mu>$ is demonstrated for the full Run 2 $pp$ data taking period at $\sqrt{s}=$13~TeV.