Search for CP violation in $D^{\pm }\to K_{\mathrm{S}}^0{K}^{\pm }$ and $D_s^{\pm }\to K_{\mathrm{S}}^0\ddot{I}{€}^{\pm }$ decays

Abstract

A search for \CP violation in Cabibbo-suppressed $D^{\pm }\to K_{\mathrm{S}}^0{K}^{\pm }$ and $D_s^{\pm }\to K_{\mathrm{S}}^0\ddot{I}{€}^{\pm }$ decays is performed using $pp$ collision data, corresponding to an integrated luminosity of 3~fb${}^{-1}$, recorded by the LHCb experiment. The individual $CP$-violating asymmetries are measured to be \begin{eqnarray*} \mathcal{A}_{CP}^{D^{\pm}\rightarrow K^0_{\mathrm{S}} K^{\pm}} & = & (+0.03 \pm 0.17 \pm 0.14) \% \mathcal{A}_{CP}^{D^{\pm}_{s}\rightarrow K^0_{\mathrm{S}} π^{\pm}} & = & (+0.38 \pm 0.46 \pm 0.17) \%, \end{eqnarray*} assuming that $CP$ violation in the Cabibbo-favoured decays is negligible. A combination of the measured asymmetries for the four decay modes $D_{(s)}^{\pm }\to K_{\mathrm{S}}^0{K}^{\pm }$ and $D_{(s)}^{\pm }\to K_{\mathrm{S}}^0\ddot{I}{€}^{\pm }$ gives the sum \[ \mathcal{A}_{CP}^{D^{\pm}\rightarrow K^0_{\mathrm{S}} K^{\pm}} + \mathcal{A}_{CP}^{D^{\pm}_{s}\rightarrow K^0_{\mathrm{S}} π^{\pm}} = (+0.41 \pm 0.49 \pm 0.26) \%. \] In all cases, the first uncertainties are statistical and the second systematic. The results represent the most precise measurements of these asymmetries to date and show no evidence for CP violation.