Dalitz Plot Analysis and Extraction of Spin Density Matrix Elements for the Ω → 3Π Decay

At the Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson National Laboratory (JLab), $\omega$ vector-mesons were photo-produced off a fixed, liquid-hydrogen target during the 2009 run-period via the reaction $\gamma p \rightarrow p \omega$. The charged final-state particles from the $\omega$~resonance decays were detected by the CEBAF Large Acceptance Spectrometer (CLAS). With a combination of measurements which involved the use of time and energy-deposit counters as well as reconstructed drift chamber (DC) tracks, the 4-momenta and vertices of the initial- and charged final-state particles were determined. Subsequent to reconstruction, event selection, kinematic fitting, signal and background separation, and detector efficiency simulation of the data for the three-pion final-state, i.e. $\omega \rightarrow \pi^+~\pi^-~(\pi^0)$, the Florida State University (FSU) Experimental Hadronic Nuclear Group has extracted the differential production cross section.\\ \indent With such data and the measured differential cross section in hand, I have conducted a Dalitz plot analysis of the $\omega \rightarrow 3\pi$ decay in close cooperation with the Joint Physics Analysis Center (JPAC) at JLab. The decay probability density separates into angle-dependent and -independent factors: the Spin Density Distribution (SDD) which is proportional to the differential cross section, and the reduced decay distribution (RDD) which is proportional to the decay width, respectively. The Spin Density Matrix Elements (SDMEs) for an unpolarized beam were obtained from fitting the SDD. In addition, fits for two different RDDs, i.e. a Dalitz plot distribution and a JPAC distribution, have been underway. The former is a truncated polynomial expansion of Lorentz Invariant Dalitz plot variables. The latter was based on the isobar model of the $\omega$ decay. Having made use of sub-energy unitarity, this model accounts for both elastic and inelastic 3-body re-scattering effects. Plus, fitting this model to measured data is a first. A comparison through fit parameters of each reduced distribution is intended. Lastly, my results and as well as a discussion of future extensions to this study and the prospects for similar light-meson-decay analyses are concluded at the end of this thesis.\\