Evidence for $CP$ Violation in the Decay $D^{\mathbf{+}}\to K_S^0{\pi }^{\mathbf{+}}$

We observe evidence for $CP$ violation in the decay $D^{+}\to K_S^0{\pi }^{+}$ using a data sample with an integrated luminosity of $977{\mathrm{fb}}^{-1}$ collected by the Belle detector at the KEKB $e^{+}{e}^{-}$ asymmetric-energy collider. The $CP$ asymmetry in the decay is measured to be $(-0.363\pm 0.094\pm 0.067)\%$, which is 3.2 standard deviations away from zero, and is consistent with the expected $CP$ violation due to the neutral kaon in the final state.

Figure 1

Distributions of $M(K_S^0{\pi }^{+})$ (top) and $M(K_S^0{\pi }^{-})$ (bottom). Dots with error bars are the data while the histograms show the results of the parameterizations of the data. Open histograms represent the $D^{\pm }\to K_S^0{\pi }^{\pm }$ signal. Shaded and hatched regions are $D_s^{\pm }\to K_S^0{K}^{\pm }$ misidentification and combinatorial backgrounds, respectively.

Figure 2

$A_{ϵ}^{{\pi }^{+}}$ map in bins of $p_T^{\mathrm{lab}}$ and $\cos {\theta }^{\mathrm{lab}}$ of the ${\pi }^{+}$ obtained with the $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$ and $D^0\to K^{-}{\pi }^{+}{\pi }^0$ samples (triangles). The $A_{\mathrm{rec}}^{D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}}$ map is also shown (rectangles).

Figure 3

Measured $A_{CP}$ (top) and $A_{FB}$ (bottom) values as a function of $|\cos {\theta }_{D^{+}}^{\mathrm{c}.\mathrm{m}.\mathrm{s}.}|$. In the top plot, the dashed line is the mean value of $A_{CP}$ while the hatched band is the $\pm 1{\sigma }_{\mathrm{total}}$ interval, where ${\sigma }_{\mathrm{total}}$ is the total uncertainty.