Determination of the parton distribution functions of the proton from ATLAS measurements of differential $W$ and $Z/\gamma^*$ and $t\bar{t}$ cross sections

An analysis of ATLAS data on inclusive $W^{\pm}$ and $Z/\gamma^*$ boson production and $t\bar{t}$ production in $pp$ collisions at the LHC is reported. A fit to determine parton distribution functions (PDFs), using these data jointly with $ep$ deep-inelastic scattering data from HERA is performed and the contribution of ATLAS $t\bar{t}$ data is examined. The ATLAS $W$ and $Z$ boson data exhibit sensitivity to the valence quark distributions and the light quark sea flavour composition, whereas the top-quark pair production data have sensitivity to the gluon distribution. The $t\bar{t}$ distributions which are most sensitive to the gluon PDF are: the mass of the $t\bar{t}$ pair, $m_{tt}$, the rapidity of the $t\bar{t}$ pair, $y_{tt}$, the average top rapidity, $y_t$ and the average top transverse momentum, $p_T^t$. The impact of the $t\bar{t}$ data can be increased by fitting to more than one of these distributions simultaneously. For this to be possible the full information on systematic and statistical correlations between the data points in different spectra is necessary. The information on the correlations of systematic uncertainties was supplied in the original publications. The information on statistical correlations, bin-to-bin within data points of a spectrum and between the data points of different spectra, is made available in this note. The impact of the top-quark pair production data using these correlations is assessed.