Measurements of $W^{\pm}$ and top-quark pair to $Z$-boson cross-section ratios at $\sqrt{s} =~$13, 8, 7 TeV with the ATLAS detector

Measurements of the $Z \rightarrow \ell^+ \ell^-$ production cross sections, where $\ell^{\pm} = e^{\pm}, \mu^{\pm}$, in proton-proton collisions at $\sqrt{s} = 13~$TeV are presented using two sets of data recorded by the ATLAS experiment at the Large Hadron Collider. The data sets correspond to a total integrated luminosity of $81~$pb$^{-1}$ and $3.2~$fb$^{-1}$ collected in 2015 using the $50~$ns and $25~$ns bunch spacing configurations, respectively. The cross section obtained with $50~$ns configuration is used for $W^{\pm}$ to $Z$ cross-section ratio measurement. The $W^+$ to $W^-$ boson production cross-section ratio is also measured. The ratios of measured fiducial cross sections for electron and muon decay channels of the $W^{\pm}$ and $Z$ boson are evaluated and compared to the Standard Model expectations of the lepton universality. Ratio of top-quark pair to $Z$-boson production cross section is measured at $\sqrt{s} = 13~$TeV using $25~$ns bunch spacing data. Similar ratios are obtained at $\sqrt{s} = 8~$TeV and $7~$TeV using the published ATLAS results corrected to a common phase space. Single ratios, at a given $\sqrt{s}$ for the two processes and at different $\sqrt{s}$ for each process, as well as double ratios of the two processes at different $\sqrt{s}$, are evaluated. The results are compared to calculations performed at next-to-next-to-leading-order accuracy using recent sets of parton distribution functions. The data used for $t \bar{t}$ to $Z$-boson cross section ratios demonstrate significant power to constrain the gluon distribution function for the Bjorken-$x$ values near 0.1 and the light-quark sea for $x < 0.02$.