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In view of the large discrepancy about the associated production of a prompt $J/\psi$ and a $Z$ boson between the ATLAS data at $\sqrt{s}=8$ TeV and theoretical predictions for Single Parton Scattering (SPS) contributions, we perform an evaluation of the corresponding cross section at one loop accuracy (Next-to-Leading Order, NLO) in a quark-hadron-duality approach, also known as the Colour-Evaporation Model (CEM).
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