The realm of hadronic spectroscopy offers a window into the inner workings of quark-gluon inter- actions within hadrons, while providing new insights into the existence of excited hadrons. The knowledge gained from the further study of baryon resonances are manifold, as they proffer a deeper understanding of strong interactions hitherto unknown and glimpsed only through the properties of the ensuing excited baryon states. Moreover, the study of these excited states is a well-established tool implemented to further understand the non-perturbative (low-energy) regime of Quantum Chromodynamics (QCD). Nonetheless, even after decades of intense theoretical and experimental investigations, most of the predicted excited resonance states proposed by different theoretical programs, including Lattice QCD and Constituent Quark Models (CQM), have yet to be experimentally confirmed. Current theoretical calculations predict a greater number of baryon resonances than what has actually been observed. This disagreement between models and experimental studies in hadronic physics is known as the missing baryon problem. The missing resonances are excited state particles that decay quickly, and might be responsible for filling in the intermediate steps in processes such as γN → N^∗ → YZ. Excited nucleon states are typically found in broadly overlapping (across a wide range of masses and spin-parity combinations J^P ) resonances, such as N^∗ states (these have the potential to decay into a plethora of final-states YZ composed of baryons and mesons), which can account for the intermediate particle involved in the reaction. Consequently, these states are difficult to isolate via the use of cross-sectional data alone. Therefore, it becomes necessary to introduce a set of polarization observables, as they are an instrumental tool in the disentanglement process of contributing single resonant and non-resonant amplitudes, leading to the identification of the missing baryons. It is theorized that Nucleon (N^∗) resonances can decay into final-state pairs like the ΛK or KΣ channels. The data employed in this thesis was recorded at the Thomas Jefferson National Accelerator Facility (JLab) under the CLAS g12 experiment as part of their N^∗ spectroscopy program, via the use of the CEBAF Large Acceptance Spectrometer (CLAS) detector. This experiment recorded photoproduction data from the application of a circularly-polarized photon beam incident on an unpolarized liquid Hydrogen (lH 2 ) target, using a photon energy range of 1.1 < Eγ < 5.4 GeV. In this work we determined the beam-recoil polarization transfer observables Cx and Cz , as well as the hyperon-recoil polarization observable P , for the photoproduction reaction γp → K^0 Σ^+ , within the energy range 1.15 < E γ < 3.0 GeV. Each of the aforementioned observables {Cx, P, Cz } were extracted individually via the use of a linear fit, and simultaneously via the implementation of a Maximum Likelihood fit. The main motivation behind studying the photoproduction reaction γp → K^0 Σ^+ stems from the fact that it is relatively understudied amongst the other isospin-related KΣ channels. Furthermore, the K^0 Σ^+ final-state has no published measurements of its double-polarization observables, thus the work herein presented will be the first of its kind in providing results for the observables Cx and Cz , which will in turn aid in the determination of contributing baryon resonances.
