Search for $CP$ Violation in the Decays $D^0\to K_S^0{P}^0$

We have searched for $CP$ violation in the decays $D^0\to K_S^0{P}^0$ where $P^0$ denotes a neutral pseudoscalar meson that is either a ${\pi }^0$, $\eta$, or ${\eta }^{\prime }$ using KEKB asymmetric-energy $e^{+}{e}^{-}$ collision data corresponding to an integrated luminosity of $791{\mathrm{fb}}^{-1}$ collected with the Belle detector. No evidence of significant $CP$ violation is observed. We report the most precise $CP$ asymmetry measurement in the decay $D^0\to K_S^0{\pi }^0$ to date: $A_{CP}^{D^0\to K_S^0{\pi }^0}=(-0.28\pm 0.19\pm 0.10)\%$. We also report the first measurements of $CP$ asymmetries in the decays $D^0\to K_S^0\eta$ and $D^0\to K_S^0{\eta }^{\prime }$: $A_{CP}^{D^0\to K_S^0\eta }=(+0.54\pm 0.51\pm 0.16)\%$ and $A_{CP}^{D^0\to K_S^0{\eta }^{\prime }}=(+0.98\pm 0.67\pm 0.14)\%$, respectively.

Figure 1

Distributions of the $M(D^{*})-M(D)$ for the studied decay modes. Left plots show the $M(D^{*+})-M(D^0)$ and right plots show the $M(D^{*-})-M({\overline{D}}^0)$. Top plots are for the $K_S^0{\pi }^0$, middle plots for the $K_S^0\eta$, and bottom plots for the $K_S^0{\eta }^{\prime }$ final states. Points with error bars are the data, and the histograms show the results of the parametrizations of the data. Hatched areas are the background contributions.

Figure 2

$A_{ϵ}^{{\pi }_s^{+}}$ map in bins of $p_T^{\mathrm{lab}}$ and $\cos {\theta }^{\mathrm{lab}}$ of the ${\pi }_s^{+}$ obtained with around $11\times {10}^6$ untagged and $2.5\times {10}^6$ tagged events (triangles). The $A_{\mathrm{rec}}^{\mathrm{tagged}}$ map obtained with tagged candidates is also shown (rectangles).

Figure 3

Measured $A_{CP}$ (left) and $A_{FB}$ (right) values as a function of $|\cos {\theta }_{D^{*+}}^{\mathrm{c}.\mathrm{m}.\mathrm{s}.}|$. Top plots are for $K_S^0{\pi }^0$, middle plots for $K_S^0\eta$, and bottom plots for $K_S^0{\eta }^{\prime }$ final states. The dashed curves show the leading-order prediction for $A_{FB}^{c\overline{c}}$.