## Wayne State University Dissertations

#### Title

Multiple Dalitz Plot Analysis At Cleo-C

WSU Access

January 2016

Dissertation

Ph.D.

#### Department

Physics and Astronomy

Dalitz Plot analysis is a standard technique for the study of weak hadronic 3-body decays. This technique allows us to extract the relative amplitudes, phases, and fit fractions of the resonances that are the primary product of such decays. A Dalitz analysis is complicated by the presence of two or more interfering resonances that appear at the same place on the plot. In this analysis I attempt to resolve the $K^{0}_{s} a_{0}(980)^{0}$ and $K^{0}_{s} f_{0}(980)$ in the decay of $D^{0} \to K^{0}_{s} K^{+} K^{-}$. Using the $K^{0}_{s} a_{0}(980)^{0}$ resonance found in $D^{0} \to K^{0}_{s} \pi^{0} \eta$, I compare equating a resonance in an interfering decay channel with a non--interfering channel by fit fraction or amplitude. I use the 818 $pb^{-1}$ of CLEO-c data collected a $\psi(3770)$ energies to perform the Dalitz plot analysis of $D^{0} \to K^{0}_{s} \pi^{0} \eta$ and $D^{0} \to K^{0}_{s} K^{+} K^{-}$. I find large fractions from both $K^{0}_{s} a_{0}(980)^{0}$ and $K^{0}_{s} f_{0}(980)$ that destructively interfere to leave the $K^{0}_{s} \phi(1020)$ as the dominant resonance on the plot.