Studies of the decays D^0 \rightarrow K_S^0K^-π^+ and D^0 \rightarrow K_S^0K^+π^-
The first measurements of the coherence factor R_{K_S^0Kπ} and the average strong--phase difference δ^{K_S^0Kπ} in D^0 \to K_S^0 K^\mpπ^\pm decays are reported. These parameters can be used to improve the determination of the unitary triangle angle γ 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 ψ(3770) resonance. The measured values are R_{K_S^0Kπ} = 0.70 \pm 0.08 and δ^{K_S^0Kπ} = (0.1 \pm 15.7)$^\circ$ for an unrestricted kinematic region and R_{K*K} = 0.94 \pm 0.12 and δ^{K*K} = (-16.6 \pm 18.4)$^\circ$ for a region where the combined K_S^0 π^\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^+π^-)/{B}(D^0 \rightarrow K_S^0K^-π^+) is determined to be 0.592 \pm 0.044 (stat.) \pm 0.018 (syst.), which is more precise than previous measurements.