Search for $CP$ violation in $D^{\pm}\rightarrow K^0_S K^{\pm}$ and $D^{\pm}_{s}\rightarrow K^0_S \pi^{\pm}$ decays

A search for $CP$ violation in Cabibbo-suppressed $D^{\pm}\rightarrow K^0_S K^{\pm}$ and $D^{\pm}_{s}\rightarrow K^0_S \pi^{\pm}$ 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_S K^{\pm}} & = & (+0.03 \pm 0.17 \pm 0.14) \% \\ \mathcal{A}_{CP}^{D^{\pm}_s\rightarrow K^0_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 $D^{\pm}_{(s)}\rightarrow K^0_S K^{\pm}$ and $D^{\pm}_{(s)}\rightarrow K^0_S \pi^{\pm}$ gives the sum \[ \mathcal{A}_{CP}^{D^{\pm}\rightarrow K^0_S K^{\pm}}+ \mathcal{A}_{CP}^{D^{\pm}_s\rightarrow K^0_S \pi^{\pm}} = (+0.41 \pm 0.49 \pm 0.26) \%. \] 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.