Abstract
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). This work is motivated by (i) the extremely disparate predictions based on the existing NRQCD fits conjugated with the absence of a full NLO NRQCD computation and (ii) the fact that we believe that such an evaluation provides a likely upper limit of the SPS cross section. In addition to these theory improvements, we argue that the ATLAS estimation of the Double Parton Scattering (DPS) yield may be underestimated by a factor as large as 3 which then reduces the size of the SPS yield extracted from the ATLAS data. Our NLO SPS evaluation also allows us to set an upper limit on $\sigma_{\rm eff}$ driving the size of the DPS yield. Overall, the discrepancy between theory and experiment may be smaller than expected, which calls for further analyses by ATLAS and CMS, for which we provide predictions, and for full NLO computations in other models. As an interesting side product of our analysis, we have performed the first NLO computation of $d\sigma / dP_T$ for prompt single-$J/\psi$ production in the CEM from which we have fit the CEM non-pertubative parameter at NLO using the most recent ATLAS data.