The precision of the theoretical predictions for interaction rates in high-energy collisions has increased dramatically over the past years, promptingus to test the prediction at a high precision level, with the option to find signs for new physics in deviations from the current models. The project is supposed to measure processes where jets of hadrons are produced in association with the neutral massive carriers of the weak force, the Z bosons. Since they result in similar final states as the production of new particles they have to be described at a high precision, lest we confuse them with the latter. The focus of the thesis is on a special class of these processes where the hadronic jets are initiated by heavy B or D mesons. The description of such processes provides additional challenges for theory and several so far barely tested approaches are advertised to predict them with high precision. The process is also sensitive to the bottom and charm content of the proton. The measurement is supposed to be performed in proton-proton colision data collected in the years 2015-2018 at the ATLAS experiment at the Large Hadron Collider at CERN.