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A measurement of the differential cross-section of $pp \rightarrow Z/\gamma^{*}(\rightarrow e^{+}e^{-})$~+~jet production and a study of the jet quark-gluon decomposition are presented. The data of 21.3 $\mathrm{fb^{-1}}$ collected with the ATLAS detector at the Large Hadron Collider in 2012 at the centre-of-mass energy $\sqrt{s} = 8$~TeV are used.The double-differential $pp \rightarrow Z/\gamma^{*}(\rightarrow e^{+}e^{-})$~+~jet cross-section is measured as a function of the absolute rapidity and the transverse momentum of jets. The jet quark-gluon decomposition study is performed in bins of the transverse momentum and the absolute rapidity of the highest-$p_{T}$ jet. The possibility to distinguish between quark-initiated and gluon-initiated jets is especially important for beyond Standard Mode searches, where a lot of signal processes have quarks in the final states, while background processes in Quantum Chromodynamic have mostly gluons. The performance of the discrimination between these two types of jets using different jet properties is studied using data-driven techniques with purified quark-like and gluon-like jet samples. The $pp \rightarrow Z/\gamma^{*}(\rightarrow e^{+}e^{-})$~+~jet production provides an important test of perturbative Quantum Chromodynamics and is an important background for many Standard Model processes and beyond Standard Model searches. In addition, the measurement of the $pp \rightarrow Z/\gamma^{*}(\rightarrow e^{+}e^{-})$~+~jet cross section as a function of the absolute rapidity and the transverse momentum of inclusive jets provides constraints on the uncertainties on the parton distribution functions. The rapidity of jets provides the information on the fraction of the initial proton’s momentum carried by the interacting partons, which provides the sensitivity to the parton distribution functions, while the transverse momentum of jets allows to probe different transfer momentum scales.The measured cross-section is compared to the predictions from Monte Carlo generators based on leading order matrix elements and supplemented by parton showers, where the predictions are normalised to the inclusive $pp \rightarrow Z/\gamma^{*}\rightarrow e^{+}e^{-}$ cross-section calculated at the next-to-next-to-leading order. The predictions are in a good agreement with the measured cross-section within the uncertainty on the measurement, except particular absolute rapidity and transverse momentum regions

Measurements of Z boson plus jet production cross section using $\sqrt{s}=8$ TeV data and studies of jet quark-gluon decomposition