Methods to quantify the performance of the primary vertex reconstruction in the ATLAS experiment under high luminosity conditions

Presented in this contribution are methods currently developed and used by the ATLAS collaboration to measure the performance of the primary vertex reconstruction algorithms. With the increasing instantaneous luminosity at the LHC, many proton-proton collisions occur simultaneously in one bunch crossing. The correct identification of the primary vertex from a hard scattering process and the knowledge of the number of additional pile-up interactions is crucial for many physics analyses. Under high pile-up conditions, additional effects like splitting one vertex into many or reconstructing several interactions as one also become sizable effects. The mathematical methods, their software implementation, and studies presented in this contribution are methods currently developed and used by the ATLAS collaboration to measure the performance of the primary vertex reconstruction algorithms. Statistical methods based on data and Monte Carlo simulation are both used to disentangle and understand the different contributions