Improved branching-fraction measurements of $B^0_{(s)} \to K_S^0 h^+ h^{'-}$ decays and first observation of $B^0_{s} \to K_S^0 K^+ K^-$

This paper presents a study of the charmless three-body decays ${B^0_{(s)} \to K_{\mathrm{S}}^0 h^+ h^{\prime -}}$ (where $h^{(\prime)} = \pi, K$), using a sample of $pp$ collision data collected by the LHCb experiment, corresponding to an integrated luminosity of $9\mbox{\,fb}^{-1}$. The decay ${B^0_s \to K_{\mathrm{S}}^0 K^+ K^-}$ is observed for the first time, and the following ratios of branching fractions are measured: \begin{alignat*}{6}&\frac{{\cal B}(B^0 \to K^0_{\mathrm{S}} K^+ K^-)}{{\cal B}(B^0 \to K^0_{\mathrm{S}} \pi^+\pi^-)}&&= 0.578&&\pm 0.007&&\pm 0.017\,,&\frac{{\cal B}(B^0 \to K^0_{\mathrm{S}} K^\pm\pi^\mp)}{{\cal B}(B^0 \to K^0_{\mathrm{S}} \pi^+\pi^-)}&&= 0.1363&&\pm 0.0035&&\pm 0.0051\,,&\frac{{\cal B}(B^0_s \to K^0_{\mathrm{S}} \pi^+\pi^-)}{{\cal B}(B^0 \to K^0_{\mathrm{S}} \pi^+\pi^-)}&&= 0.269&&\pm 0.011&&\pm 0.015&&\pm 0.008\,,&\frac{{\cal B}(B^0_s \to K^0_{\mathrm{S}} K^+ K^-)}{{\cal B}(B^0 \to K^0_{\mathrm{S}} \pi^+\pi^-)}&&= 0.0303&&\pm 0.0041&&\pm 0.0025&&\pm 0.0009\,,&\frac{{\cal B}(B^0_s \to K^0_{\mathrm{S}} K^\pm\pi^\mp)}{{\cal B}(B^0 \to K^0_{\mathrm{S}} \pi^+\pi^-)}&&= 1.818&&\pm 0.021&&\pm 0.031&&\pm 0.056\,, \end{alignat*} where the uncertainties are statistical, systematic, and due to knowledge of the ratio of hadronisation fractions of the $B^0_s$ and $B^0$ mesons, respectively.