Measurements of the $t\bar{t}$ production cross-section in the dilepton and lepton-plus-jets channels and of the ratio of the $t\bar{t}$ and $Z$ boson cross-sections in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector

This note describes measurements of the inclusive top-quark pair production cross-section with a data sample of 85 pb$^{-1}$ of proton-proton collisions at a centre-of-mass energy of 13 TeV, collected in 2015 by the ATLAS detector. Two measurements are presented, one with an opposite-sign same-flavour lepton pair in the final state and one with a single lepton and at least four jets in the final state. In both measurements at least one jet is required to be identified as originating from a $b$-quark. In addition, a measurement of the ratio of the $t\bar{t}$ and $Z$-boson production cross-sections is presented, based on a measurement of the $t\bar{t}$ cross-section in the $e\mu$ dilepton final state. All results are consistent with theoretical QCD calculations at next-to-next-to-leading order.