Studies of the resonance structure in $D^0\to K_S^0{K}^{\pm }{\pi }^{\mp }$ decays

Amplitude models are applied to studies of resonance structure in $D^0\to K^0_S K^- \pi^+$and$D^0\to K^0_S K^+ \pi^-$decaysusing$pp$ collision data corresponding to an integrated luminosity of $3.0{\mathrm{f}\mathrm{b}}^{-1}$ collected by the LHCb experiment. Relative magnitude and phase information is determined, and coherence factors and related observables are computed for both the whole phase space and a restricted region of $100\mathrm{M}\mathrm{e}\mathrm{V}\mathrm{/}{c}^2$ around the $K^{\ast }(892{)}^{\pm }$ resonance. Two formulations for the $K\pi$ $S$-wave are used, both of which give a good description of the data. The ratio of branching fractions $$\mathcal{B}$(D^0\to K^0_S K^+ \pi^-)/$\mathcal{B}$(D^0\to K^0_S K^- \pi^+)$ismeasuredtobe$0.655\pm0.004,($\text{stat}$)\pm0.006,($\text{syst}$)$ over the full phase space and $0.370\pm 0.003(\text{stat})\pm 0.012(\text{syst})$ in the restricted region. A search for $CP$ violation is performed using the amplitude models and no significant effect is found. Predictions from $SU(3)$ flavor symmetry for $K^{\ast }(892)K$ amplitudes of different charges are compared with the amplitude model results.