Measurement of lepton kinematic distributions in the $e\mu$ decay channel of $t\bar{t}$ events observed in $pp$ collisions at $\sqrt{s}=13\;$TeV with the ATLAS detector

The differential and double differential distributions of kinematic variables of leptons from decays of top quark pairs are measured using the full LHC Run II sample of data collected with the ATLAS detector. The data were collected at a $pp$ collision energy of $\sqrt{s}=13$ TeV, corresponding to an integrated luminosity of 139 fb$^{-1}$. The measurements use events containing an opposite charged $e\mu$ pair and $b$-tagged jets. They are compared with predictions of $t\bar{t}$ Monte Carlo event generators. While no generator is found to be consistent with all distributions, some improvement in the agreement with measurements of the lepton $p_T$ distributions is obtained by reweighting the $t\bar{t}$ sample so as to reproduce top-antitop quark $p_T$ distribution from an NNLO calculation. The inclusive top quark pair production cross-section is measured as well, both in a fiducial region and in the full phase-space. The total inclusive cross-section is found to be \[ \sigma_{$t\bar{t}$} = 836 \pm 1\;(\textrm{stat}) \pm 12\;(\textrm{syst}) \pm 16\;(\textrm{lumi}) \pm 2\; (\textrm{beam})\ \textrm{pb}, \] where the uncertainties are due to statistics, theoretical and experimental systematic effects, the integrated luminosity and the beam energy. This is in excellent agreement with the theoretical expectation.