Measurement of the $\mathrm{t}\overline{\mathrm{t}}$ production cross section, the top quark mass, and the strong coupling constant using dilepton events in pp collisions at $\sqrt{s} =$ 13 TeV

A measurement of the top quark-antiquark pair production cross section $\sigma_{\mathrm{t\overline{t}}}$ in proton-proton collisions at a centre-of-mass energy of 13 TeV is presented. The data correspond to an integrated luminosity of 35.9 fb$^{-1}$, recorded by the CMS experiment at the CERN LHC in 2016. Dilepton events (e$^\pm\mu^\mp$, $\mu^+\mu^-$, e$^+$e$^-$) are selected and the cross section is measured from a likelihood fit. For a top quark mass parameter in the simulation of $m^{\mathrm{MC}}_{\mathrm{t}} =$ 172.5 GeV the fit yields a measured cross section $\sigma_{\mathrm{t\overline{t}}} =$ 803 $\pm$ 2 (stat) $\pm$ 25 (syst) $\pm$ 20 (lumi) pb, in agreement with the expectation from the standard model calculation at next-to-next-to-leading order. A simultaneous fit of the cross section and the top quark mass parameter in the POWHEG simulation is performed. The measured value of $m^{\mathrm{MC}}_{\mathrm{t}} =$ 172.33 $\pm$ 0.14 (stat) $^{+0.66}_{-0.72}$ (syst) GeV is in good agreement with previous measurements. The resulting cross section is used, together with the theoretical prediction, to determine the top quark mass and to extract a value of the strong coupling constant with different sets of parton distribution functions.