Partial Wave Analysis of Meson Resonances That Decay $K^\ast\bar{K}$ Using Data from the GlueX Experiment

The GlueX experiment housed in Hall D of the Thomas Jefferson National Laboratory was created to map the light meson spectrum in order to contribute to the Standard Model of particle physics by strengthening our understanding of the strong interaction. GlueX is a medium-energy photoproduction experiment that utilizes a linearly polarized photon beam to create hadronic forms of matter. By mapping the light meson spectrum, the GlueX collaboration hopes to identify meson states forbidden by the Constituent Quark Model. As a main research objective, the GlueX collaboration is searching for hybrid $q\bar{q}g$ meson states that exhibit exotic quantum numbers. One hybrid meson candidate is the $\eta'_1$, which is predicted to decay to $K^\ast\bar{K}$ and have a mass near $2.3~\mathrm{GeV}$ (\citeauthor{qn_exotic_status}, \citeyear{qn_exotic_status}; \citeauthor{hybrid_mesons}, \citeyear{hybrid_mesons}). At this time, very few meson states have been identified in the $2.0~\mathrm{GeV}$ mass region. This dearth of evidence for existing states requires any tool developed to search for meson states above $2.0~\mathrm{GeV}$ must be verified by looking at known meson states. In order to search for the $\eta'_1$ hybrid meson candidate in $\gamma p \rightarrow pK^+K^-\gamma\gamma$ events, meson states decaying $K^\ast\bar{K}$ that contribute to the low mass region must be identified, defined in this document as particles having masses between $1400$ and $1600~\mathrm{MeV}$. Identifying what meson states exist in the low mass region is also critical to mapping the light meson spectrum and determining the quark-gluonic content of those meson states. The results of a partial wave analysis (PWA) of $\gamma p \rightarrow pX$ where $X\rightarrow K^\ast\bar{K}$ from $\gamma p \rightarrow pK^+K^-\gamma\gamma$ events in GlueX are presented. In the $J=0$ invariant mass distribution, the $\eta(1405)$ and $\eta(1475)$ are identified, adding to the debate as to whether two pseudoscalar mesons exist in the low mass region. For the $J=1$ distribution, the $f_1(1420)$ and $f_1(1510)$ axial vector mesons are seen, where the former helps further elaborate on the $E\iota$ puzzle of the twentieth century \citep{E_iota_puzzle}. With respect to the controversy of meson states in the low mass region, evidence for the existence of the $f_2(1430)$ meson is strengthened in the $J=2$ distribution, and the $f'_2(1525)$ state is seen. This work lays a foundation for the ASU Meson Physics Group to continue a wider search for hybrid mesons in the $\gamma p \rightarrow pK^+K^-\gamma\gamma$ reaction topology.