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 $x<0.02$.
Correlation coefficients amongst the combined (Z/gamma^* -> l+ l-) where (l = e, mu) fiducial cross section and ttbar total cross section at 13, 8, and 7TeV, omitting the common normalisation uncertainty due to the luminosity calibration and beam energy.
Z-boson and ttbar production cross-section single ratios at 13, 8, 7TeV. The beam-energy uncertainty, which largely cancels in the ratios, is included in the systematic uncertainty. In the first column, the total (TOT) cross sections are used for both numerator and denominator. In the second column, the total cross section is used for the numerator while the fiducial (FID) cross section is used for the denominator. In the third column, the fiducial cross sections are used for both numerator and denominator. Apart for the MZ requirement, the kinematic fiducial requirements listed below apply only to the fiducial cross sections. The luminosity uncertainty almost entirely cancels in some of the ratio measurements.
Z-boson and ttbar production cross-section double ratios at 13, 8, 7TeV. The beam-energy uncertainty, which largely cancels in the ratios, is included in the systematic uncertainty. In the first column, the total (TOT) cross sections are used for both ttbar and Z processes. In the second column, the total cross section is used for ttbar while the fiducial (FID) cross section is used for Z. In the third column, the fiducial cross sections are used for both ttbar and Z. Apart for the MZ requirement, the kinematic fiducial requirements listed below apply only to the fiducial cross sections.
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