Studies of the decays D^0 \rightarrow K_S^0K^-\pi^+ and D^0 \rightarrow K_S^0K^+\pi^-

The first measurements of the coherence factor R_{K_S^0K\pi} and the average strong--phase difference \delta^{K_S^0K\pi} in D^0 \to K_S^0 K^\mp\pi^\pm decays are reported. These parameters can be used to improve the determination of the unitary triangle angle \gamma in B^- \rightarrow \widetilde{D}K^-$ decays, where $\widetilde{D}$ is either a D^0 or a D^0-bar meson decaying to the same final state, and also in studies of charm mixing. The measurements of the coherence factor and strong-phase difference are made using quantum-correlated, fully-reconstructed D^0D^0-bar pairs produced in e^+e^- collisions at the \psi(3770) resonance. The measured values are R_{K_S^0K\pi} = 0.73 \pm 0.08 and \delta^{K_S^0K\pi} = (8.3 \pm 15.2)$^\circ$ for an unrestricted kinematic region and R_{K*K} = 1.00 \pm 0.16 and \delta^{K*K} = (26.5 \pm 15.8)$^\circ$ for a region where the combined K_S^0 \pi^\pm invariant mass is within 100 MeV/c^2 of the K^{*}(892)^\pm mass. These results indicate a significant level of coherence in the decay. In addition, isobar models are presented for the two decays, which show the dominance of the K^*(892)^\pm resonance. The branching ratio {B}(D^0 \rightarrow K_S^0K^+\pi^-)/{B}(D^0 \rightarrow K_S^0K^-\pi^+) is determined to be 0.592 \pm 0.044 (stat.) \pm 0.018 (syst.), which is more precise than previous measurements.