Measurement of the Branching Ratios of 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 Γ(D⁺ → K_SK⁻π⁺π⁺)/Γ(D⁺ → K_Sπ⁺π⁺π⁻) = 0.0768 ± 0.0041 ± 0.0032. We make the first observation of three new decay modes with branching ratios Γ(D⁺ → K_SK⁺π⁺π⁻)/Γ(D⁺ → K_Sπ⁺π⁺π⁻) = 0.0562 ± 0.0039 ± 0.0040, Γ(D⁺ → K_SK⁺K⁻π⁺)/Γ(D⁺ → K_Sπ⁺π⁺π⁻) = 0.0077 ± 0.0015 ± 0.0009, and Γ(D⁺_s → K_SK⁺π⁺π⁻)/Γ(D⁺_s → K_SK⁻π⁺π⁺) = 0.586 ± 0.052 ± 0.043, where in each case the first error is statistical and the second error is systematic.