Search for $CP$ violation in the decays $D^{\pm }\to K_S^0{K}^{\pm }$, $D_s^{\pm }\to K_S^0{K}^{\pm }$, and $D_s^{\pm }\to K_S^0{\pi }^{\pm }$

We report a search for $CP$ violation in the decay modes $D^{\pm }\to K_S^0{K}^{\pm }$, $D_s^{\pm }\to K_S^0{K}^{\pm }$, and $D_s^{\pm }\to K_S^0{\pi }^{\pm }$ using a data set corresponding to an integrated luminosity of $469{\mathrm{fb}}^{-1}$ collected with the BABAR detector at the PEP-II asymmetric energy $e^{+}{e}^{-}$ storage rings. The decay rate $CP$ asymmetries, $A_{CP}$, are determined to be $(+0.13\pm 0.36(\mathrm{stat})\pm 0.25(\mathrm{syst}))\%$, $(-0.05\pm 0.23(\mathrm{stat})\pm 0.24(\mathrm{syst}))\%$, and $(+0.6\pm 2.0(\mathrm{stat})\pm 0.3(\mathrm{syst}))\%$, respectively. These measurements are consistent with zero, and also with the Standard Model prediction [$(-0.332\pm 0.006)\%$ for the $D^{\pm }\to K_S^0{K}^{\pm }$ and $D_s^{\pm }\to K_S^0{K}^{\pm }$ modes, and $(+0.332\pm 0.006)\%$ for the $D_s^{\pm }\to K_S^0{\pi }^{\pm }$ mode]. They are the most precise determinations to date.

Figure 1

Invariant mass distribution for (a) $D^{\pm }\to K_S^0{K}^{\pm }$, (b) $D_s^{\pm }\to K_S^0{K}^{\pm }$, and (c) $D_s^{\pm }\to K_S^0{\pi }^{\pm }$ candidates (points with error bars). The solid curve shows the result of the fit to the data. The dashed curve represents the sum of all background contributions, while the dotted curve indicates combinatorial background only.

Figure 2

(Top) The ratio between the detection efficiency for ${\pi }^{+}$ and ${\pi }^{-}$, and (bottom) the corresponding statistical errors. The values are computed using the numbers of ${\pi }^{+}$ and ${\pi }^{-}$ tracks in the selected control sample.

Figure 3

(Top) The ratio between the detection efficiency for $K^{+}$ and $K^{-}$, and (bottom) the corresponding statistical errors. The values are computed using the numbers of $K^{+}$ and $K^{-}$ tracks in the selected control sample.

Figure 4

$CP$ asymmetry, $A_{CP}$, for (a) $D^{\pm }\to K_S^0{K}^{\pm }$, (b) $D_s^{\pm }\to K_S^0{K}^{\pm }$, and (c) $D_s^{\pm }\to K_S^0{\pi }^{\pm }$ as a function of $|\cos {\theta }_D^{*}|$ in the data sample. The solid line represents the central value of $A_{CP}$ and the gray band is the $\pm 1\sigma$ interval, both obtained from a ${\chi }^2$ minimization assuming no dependence on $|\cos {\theta }_D^{*}|$. The corresponding forward-backward asymmetries, $A_{\mathrm{FB}}$, are shown in (d)–(f).