Improved branching-fraction measurements of $B_{(s)}^0\to K_S^0{h}^{+}{h}^{{}^{\mathrm{\prime }}-}$ decays and first observation of $B_s^0\to K_S^0{K}^{+}{K}^{-}$

This paper presents a study of the charmless three-body decays $B_{(s)}^0\to K_{\mathrm{S}}^0{h}^{+}{h}^{\mathrm{\prime }-}$ (where $h^{(\mathrm{\prime })}=\pi ,K$), using a sample of $pp$ collision data collected by the LHCb experiment, corresponding to an integrated luminosity of $9f{b}^{-1}$. The decay $B_s^0\to K_{\mathrm{S}}^0{K}^{+}{K}^{-}$ 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_{$\mathrm{S}$} π^+π^-)} &&= 0.578 &&\pm 0.007 &&\pm 0.017,, &\frac{{\cal B}(B^0 \to K^0_{$\mathrm{S}$} K^\pmπ^\mp)}{{\cal B}(B^0 \to K^0_{$\mathrm{S}$} π^+π^-)} &&= 0.1363 &&\pm 0.0035 &&\pm 0.0051,, &\frac{{\cal B}(B^0_s \to K^0_{$\mathrm{S}$} π^+π^-)}{{\cal B}(B^0 \to K^0_{$\mathrm{S}$} π^+π^-)} &&= 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_{$\mathrm{S}$} π^+π^-)} &&= 0.0303 &&\pm 0.0041 &&\pm 0.0025 && \pm 0.0009,, &\frac{{\cal B}(B^0_s \to K^0_{$\mathrm{S}$} K^\pmπ^\mp)}{{\cal B}(B^0 \to K^0_{$\mathrm{S}$} π^+π^-)} &&= 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 $B_s^0$ and $B^0$ mesons, respectively.