Search for long-lived particles decaying in the muon spectrometer of the ATLAS detector at the LHC

This thesis presents the results of two searches for long-lived, weakly-interacting neutral particles. These searches are performed with 22.1 fb$^{-1}$ of proton--proton collision data collected with the ATLAS detector at the Large Hadron Collider. The first search is for events with a single displaced muon spectrometer (MS) vertex and two, high-energy jets. The second search is for events with two displaced MS vertices, requiring no prompt activity. The individual power of these searches depends on the model they are being applied to, and two models are studied: Stealth Supersymmetry, and Standard Model Higgs boson decays to long-lived, neutral scalars. The former model is studied in the context of both searches, while the latter is only studied in the two displaced MS vertex search. No excess of events over the expected background is found in either search, so 95\% confidence level limits are set. For Stealth Supersymmetry, limits are also presented for the combination of the two studied topologies.