Measurement of the Branching Ratios of ${\mathit{D}}^{+}$ and $D_s^{+}$ Hadronic Decays to Four-Body Final States Containing a $K_S$

We have studied hadronic four-body decays of $D^{+}$ and $D_s^{+}$ mesons with a $K_S$ in the final state using data recorded during the 1996–1997 fixed-target run of the Fermilab high energy photoproduction experiment FOCUS. We report a new branching ratio measurement of $\Gamma (D^{+}\to K_S{K}^{-}{\pi }^{+}{\pi }^{+})/\Gamma (D^{+}\to K_S{\pi }^{+}{\pi }^{+}{\pi }^{-})=0.0768\mathrm{}\pm 0.0041\pm 0.0032$. We make the first observation of three new decay modes with branching ratios $\Gamma (D^{+}\to K_S{K}^{+}{\pi }^{+}{\pi }^{-})/\Gamma (D^{+}\to K_S{\pi }^{+}{\pi }^{+}{\pi }^{-})=0.0562\mathrm{}\pm 0.0039\pm 0.0040$, $\Gamma (D^{+}\to K_S{K}^{+}{K}^{-}{\pi }^{+})/\Gamma (D^{+}\to K_S{\pi }^{+}{\pi }^{+}{\pi }^{-})=0.0077\mathrm{}\pm 0.0015\pm 0.0009$, and $\Gamma (D_s^{+}\to K_S{K}^{+}{\pi }^{+}{\pi }^{-})/\Gamma (D_s^{+}\to K_S{K}^{-}{\pi }^{+}{\pi }^{+})=0.586\mathrm{}\pm 0.052\pm 0.043$, where in each case the first error is statistical and the second error is systematic.