Precision measurement of CP violation and branching fractions in $B^{\pm }\to K_{\mathrm{S}}^0{h}^{\pm }$ $(h=\pi ,K)$ decays and search for the rare decay $B_c^{\pm }\to K_{\mathrm{S}}^0{K}^{\pm }$

The decay $B^{\pm }\to K_{\mathrm{S}}^0{\pi }^{\pm }$, with a $CP$ asymmetry expected to be close to zero in the Standard Model, is theoretically clean and sensitive to potential new physics. An analysis of the decays $B^{\pm }\to K_{\mathrm{S}}^0{\pi }^{\pm }$ and $B^{\pm }\to K_{\mathrm{S}}^0{K}^{\pm }$ is performed using proton-proton collision data collected by the LHCb experiment at a center-of-mass energy of $13\mathrm{T}\mathrm{e}\mathrm{V}$, corresponding to an integrated luminosity of $5.4{\mathrm{f}\mathrm{b}}^{-1}$. The \CP asymmetries are determined to be ${\mathcal{A}}^{CP}(B^{\pm }\to K_{\mathrm{S}}^0{\pi }^{\pm })=-0.028\pm 0.009\pm 0.009$ and ${\mathcal{A}}^{CP}(B^{\pm }\to K_{\mathrm{S}}^0{K}^{\pm })=0.118\pm 0.062\pm 0.031$, and the branching fraction ratio is measured to be $\mathcal{B}(B^{\pm }\to K_{\mathrm{S}}^0{K}^{\pm })\mathrm{/}\mathcal{B}(B^{\pm }\to K_{\mathrm{S}}^0{\pi }^{\pm })=0.055\pm 0.004\pm 0.002$, where the first uncertainties are statistical and the second are systematic. These results are the most precise measurements of these quantities to date. A search for the rare decay $B_c^{\pm }\to K_{\mathrm{S}}^0{K}^{\pm }$ is also performed. No significant signal is observed, and the upper limit on the product of the branching fraction ratio $\mathcal{B}(B_c^{\pm }\to K_{\mathrm{S}}^0{K}^{\pm })\mathrm{/}\mathcal{B}(B^{\pm }\to K_{\mathrm{S}}^0{\pi }^{\pm })$ and the fragmentation-fraction ratio $f_c\mathrm{/}{f}_u$ is set to be 0.015 (0.016) at the 90% (95%) confidence level.