Search for $CP$ Violation in the Decays $D_{(s)}^{+}\to K_S^0{\pi }^{+}$ and $D_{(s)}^{+}\to K_S^0{K}^{+}$

We have searched for $CP$ violation in the charmed meson decays $D_{(s)}^{+}\to K_S^0{\pi }^{+}$ and $D_{(s)}^{+}\to K_S^0{K}^{+}$ using $673{\mathrm{fb}}^{-1}$ of data collected with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. No evidence for $CP$ violation is observed. We report the most sensitive $CP$ asymmetry measurements to date for these decays: $A_{CP}^{D^{+}\to K_S^0{\pi }^{+}}=(-0.71\pm 0.19\pm 0.20)\%$, $A_{CP}^{D_s^{+}\to K_S^0{\pi }^{+}}=(+5.45\pm 2.50\pm 0.33)\%$, $A_{CP}^{D^{+}\to K_S^0{K}^{+}}=(-0.16\pm 0.58\pm 0.25)\%$, and $A_{CP}^{D_s^{+}\to K_S^0{K}^{+}}=(+0.12\pm 0.36\pm 0.22)\%$, where the first uncertainties are statistical and the second are systematic.

Figure 1

Invariant mass distributions for the $K_S^0{\pi }^{\pm }$ and $K_S^0{K}^{\pm }$ final states. Points with error bars (note the small size of them due to the large sample) show the data and the histograms show the results of the parametrizations of the data. Signal, peaking background, and random combinatorial background components are also shown.

Figure 2

Measured $A_{CP}$ values for $D^{+}\to K_S^0{\pi }^{+}$ in bins of ($p_{\pi }^{\mathrm{lab}}$, $\cos {\theta }_{\pi }^{\mathrm{lab}}$, $\cos {\theta }_{D^{+}}^{\mathrm{CMS}}$). Empty bins where no entries are plotted have no statistics.

Figure 3

Measured $A_{CP}$ and $A_{\mathrm{FB}}$ values for $D_{(s)}^{+}\to K_S^0{K}^{+}$ as a function of $|\cos {\theta }_{D_{(s)}^{+}}^{\mathrm{CMS}}|$. The dashed curves show the leading-order prediction for $A_{\mathrm{FB}}^{c\overline{c}}$.