Search for CP Violation in the decays ${\mathit{D}}^{+}\to K_S{\pi }^{+}$ and ${\mathit{D}}^{+}\to {K_S\mathit{K}}^{+}$

A high-statistics sample of photoproduced charm from the FOCUS experiment has been used to search for direct CP violation in the decay rates for $D^{+}\to K_S{\pi }^{+}$ and $D^{+}\to K_S{K}^{+}$. We have measured the following asymmetry parameters relative to $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$: $A_{\mathrm{CP}}\left(K_S{\pi }^{+}\right)=(-1.6\mathrm{}\pm 1.5\pm 0.9)\%$, $A_{\mathrm{CP}}\left(K_S{K}^{+}\right)=(+6.9\mathrm{}\pm 6.0\pm 1.5)\%$, and $A_{\mathrm{CP}}\left(K_S{K}^{+}\right)=(+7.1\mathrm{}\pm 6.1\pm 1.2)\%$ relative to $D^{+}\to K_S{\pi }^{+}$. We have also measured the relative branching ratios and found $\Gamma (D^{+}\to {\overline{K}}^0{\pi }^{+})/\Gamma (D^{+}\to K^{-}{\pi }^{+}{\pi }^{+})=(30.60\pm 0.46\pm 0.32)\%$, $\Gamma (D^{+}\to {\overline{K}}^0{K}^{+})/\Gamma (D^{+}\to K^{-}{\pi }^{+}{\pi }^{+})=(6.04\pm 0.35\pm 0.30)\%$, and $\Gamma (D^{+}\to {\overline{K}}^0{K}^{+})/\Gamma (D^{+}\to {\overline{K}}^0{\pi }^{+})=(19.96\pm 1.19\pm 0.96)\%$.