Search forCPviolation and a measurement of the relative branching fraction inD+→K−K+π+decays

We report on a search for the $CP$ asymmetry in the singly Cabibbo-suppressed decays $D^{+}\to K^{-}{K}^{+}{\pi }^{+}$ and in the resonant decays $D^{+}\to \varphi {\pi }^{+}$ and $D^{+}\to {\overline{K}}^{*0}{K}^{+}$ based on a data sample of $79.9{\mathrm{fb}}^{-1}$ recorded by the BABAR detector. We use the Cabibbo-favored $D_s^{+}\to K^{-}{K}^{+}{\pi }^{+}$ branching fraction as normalization in the measurements to reduce systematic uncertainties. The $CP$ asymmetries obtained are $A_{CP}(K^{-}{K}^{+}{\pi }^{\pm })=(1.4\pm 1.0(\mathrm{stat})\pm 0.8(\mathrm{syst}))\times {10}^{-2}$, $A_{CP}(\varphi {\pi }^{\pm })=(0.2\pm 1.5(\mathrm{stat})\pm 0.6(\mathrm{syst}))\times {10}^{-2}$, and $A_{CP}({\overline{K}}^{*0}{K}^{\pm })=(0.9\pm 1.7(\mathrm{stat})\pm 0.7(\mathrm{syst}))\times {10}^{-2}$. The relative branching fraction $\Gamma (D^{+}\to K^{-}{K}^{+}{\pi }^{+})/\Gamma (D^{+}\to K^{-}{\pi }^{+}{\pi }^{+})$ is also measured and is found to be $(10.7\pm 0.1(\mathrm{stat})\pm 0.2(\mathrm{syst}))\times {10}^{-2}$.