Measurement of the $t\bar{t}$ cross-section and $t\bar{t}/Z$ cross-section ratio using LHC Run 3 $pp$ collision data at a centre-of-mass energy of $\sqrt{s} = 13.6$ TeV

The inclusive top quark pair ($t\bar{t}$) production cross-section $\sigma_{t\bar{t}}$ has been measured in proton-proton collisions at $\sqrt{s} = 13.6$ TeV, using 1.2 fb${}^{-1}$ of data collected in August 2022 by the ATLAS experiment at the Large Hadron Collider. Using events with an opposite-charge $e\mu$ pair and $b$-tagged jets, and assuming Standard Model decays, the cross-section is measured to be $\sigma_{t\bar{t}} =830 \pm 12\mathrm{(stat.)}\pm 27\mathrm{(syst.)}\pm 86\mathrm{(lumi.)}$ pb. Additionally, a measurement of the ratio of the $t\bar{t}$ and the $Z$ boson production cross-section in a $Z$ fiducial phase space defined with $m_{\ell\ell} > 40$ GeV decaying into a single lepton flavour is reported, with a much reduced total uncertainty of 4.7%, thanks to the cancellation of correlated uncertainties. The $Z$ boson production cross-section is measured in $e^+e^-$ and $\mu^+\mu^-$ final states. The measured cross-section is $\sigma_{Z\to\ell\ell}^{m_{\ell\ell} > 40} = 2075 \pm 2\mathrm{(stat.)}\pm 98\mathrm{(syst.)}\pm 199\mathrm{(lumi.)}$ pb. The result for the ratio, $R_{t\bar{t}/Z} =0.400 \pm 0.006\mathrm{(stat.)}\pm 0.017\mathrm{(syst.)}\pm 0.005\mathrm{(lumi.)}$ is consistent with the Standard Model prediction using the PDF4LHC21 PDF set.