Measurements of top-quark pair to $Z$-boson cross-section ratios at $\sqrt s = 13, 8, 7$TeV with the ATLAS detector

Abstract: Ratios of top-quark pair to $Z$-boson cross sections measured from proton--proton collisions at the LHC centre-of-mass energies of $\sqrt s=13$TeV, 8TeV, and 7TeV are presented by the ATLAS Collaboration. 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 ratios are constructed using previously published ATLAS measurements of the $t\overline{t}$ and $Z$-boson production cross sections, corrected to a common phase space where required, and a new analysis of $Z \rightarrow \ell^+ \ell^-$ where $\ell=e,\mu$ at $\sqrt s=13$TeV performed with data collected in 2015 with an integrated luminosity of $3.2$fb$^{-1}$. Correlations of systematic uncertainties are taken into account when evaluating the uncertainties in the ratios. The correlation model is also used to evaluate the combined cross section of the $Z\rightarrow e^+e^-$ and the $Z\rightarrow \mu^+ \mu^-$ channels for each $\sqrt s$ value. The results are compared to calculations performed at next-to-next-to-leading-order accuracy using recent sets of parton distribution functions. The data demonstrate significant power to constrain the gluon distribution function for the Bjorken-$x$ values near 0.1 and the light-quark sea for $x<0.02$.