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

A search for \CP violation in Cabibbo-suppressed $D^{\pm}\rightarrow K^0_{$\mathrm{S}$} K^{\pm}$and$D^{\pm}{s}\rightarrow K^0{$\mathrm{S}$} \pi^{\pm}$decaysisperformedusing$pp$ 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_{$\mathrm{S}$} \pi^{\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 $D^{\pm}{(s)}\rightarrow K^0{$\mathrm{S}$} K^{\pm}$and$D^{\pm}{(s)}\rightarrow K^0{$\mathrm{S}$} \pi^{\pm}$ gives the sum $${\mathcal{A}}_{CP}^{D^{\pm }\to K_{\mathrm{S}}^0{K}^{\pm }}+{\mathcal{A}}_{CP}^{D_s^{\pm }\to K_{\mathrm{S}}^0{\pi }^{\pm }}=(+0.41\pm 0.49\pm 0.26)\mathrm{\%}\mathrm{.}$$ 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.