Exploring the Strange-Meson Spectrum with COMPASS in the Reaction $K^- + p \to K^- \pi^- \pi^+ + p$

In the naive quark-model picture, strange mesons consist of a strange and an up or down (anti)quark, which are bound by the strong interaction. Although strange mesons have been studied since more than 70 years, many parts of their excitation spectrum are still unexplored. The COMPASS experiment at CERN collected the so far world's largest sample of 720 494 exclusive events for the diffractive-scattering reaction $K^- + p \to K^- \pi^- \pi^+ + p$. This sample allows us to study strange mesons decaying into the $K^- \pi^- \pi^+$ final state. In this thesis, we present the analysis of this data sample, starting from the event selection, up to an elaborate partial-wave analysis (PWA), with which we extract the strange-meson resonances. We develop a novel method for the identification of beam kaons using the full experimentally available information, which doubles the efficiency for kaon identification compared to the previously used method. We extend the classical PWA approach by employing model-selection techniques in order to construct the partial-wave model, and by applying Bootstrapping techniques in order to improve the parameter and uncertainty estimates. Furthermore, we develop a novel approach to treat incoherent background contributions to our $K^- \pi^- \pi^+$ sample in the PWA. We perform extensive systematic studies as well as Monte Carlo studies in order to validate the analysis results. Finally, we perform a first study of the amplitudes of light mesons appearing in the $\pi^-\pi^+$ and $K^-\pi^+$ subsystems of the $K^- \pi^- \pi^+$ final state. Our analysis yields the so far most complete picture of the strange-meson spectrum coming from a single analysis. In total, we study 14 strange mesons. We find signals from well-known strange mesons, as well as indications for states that are not yet established. For example, we find indications for the $K_2(2250)$, $K_3(2320)$, and $K_4(2500)$ for the first time in a PWA of a final state other than $\Lambda \bar p$ or $\bar \Lambda p$. In addition, we find indications for three excited pseudoscalar kaons; i.e. the $K(1460)$, the $K(1630)$, and the $K(1830)$; while quark-model calculations predict only two excited states in this mass region. This hints towards an exotic nature of one of these three states. Our estimates for the masses and widths of the 14 strange mesons mostly agree with previous measurements and with quark-model calculations. Our uncertainties for most of the measured masses and widths are competitive with the corresponding so far best measurements of these parameters by previous measurements.