Searching for Long-Lived Supersymmetric Particles Using Displaced Vertices and Missing Transverse Energy with the ATLAS Detector

The Standard Model of particle physics has been extremely successful in its predictive power and has withstood a wide array of precision tests designed to expose any flaws in its description of fundamental particles. However, the Standard Model is unable to explain several phenomena observed in the universe, such as the nature of the dark matter which makes up more than 80% of the gravitationally interacting matter in the universe. Theories that extend the Standard Model with new fundamental particles have been postulated to address the questions left unanswered by the Standard Model. Many supersymmetric theories provide viable dark matter candidates. In order to more precisely test the Standard Model and its possible extensions, the ATLAS experiment at the Large Hadron Collider has been constructed to measure high energy proton-proton collisions. Long-lived particles (LLPs) are commonly predicted by extensions to the Standard Model. The decay of a LLP to charged particles within the ATLAS Inner Detector would produce tracks that are displaced from the interaction point, which could be reconstructed as a displaced vertex. This dissertation presents a search for displaced vertices with high invariant mass and high track multiplicity in events with significant missing transverse energy in the 2016-2018 data set collected by the ATLAS experiment. The observed number of events is consistent with the number expected from background processes. The results are interpreted in the context of a split-supersymmetry model with long-lived gluinos decaying to neutralinos and Standard Model quarks, and exclusion limits are set at 95% confidence level.