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

This paper presents a study of the charmless three-body decays ${B}_{(s)}^0\to {K}_{\mathrm{S}}^0{h}^{+}h{\prime}^{-}$ (where h ( ′ ) = π, K ), using a sample of pp collision data collected by the LHCb experiment during Runs 1 and 2 of the LHC, corresponding to an integrated luminosity of 9 fb − 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: ${\displaystyle \begin{array}{l}\frac{\mathcal{B}\left({B}^0\to {K}_{\mathrm{S}}^0{K}^{+}{K}^{-}\right)}{\mathcal{B}\left({B}^0\to {K}_{\mathrm{S}}^0{\pi}^{+}{\pi}^{-}\right)}=0.578\pm 0.007\pm 0.017,\\ {}\frac{\mathcal{B}\left({B}^0\to {K}_{\mathrm{S}}^0{K}^{\pm }{K}^{\mp}\right)}{\mathcal{B}\left({B}^0\to {K}_{\mathrm{S}}^0{\pi}^{+}{\pi}^{-}\right)}=0.1363\pm 0.0035\pm 0.051,\\ {}\begin{array}{l}\frac{\mathcal{B}\left({B}_s^0\to {K}_{\mathrm{S}}^0{\pi}^{+}{\pi}^{-}\right)}{\mathcal{B}\left({B}^0\to {K}_{\mathrm{S}}^0{\pi}^{+}{\pi}^{-}\right)}=0.269\pm 0.011\pm 0.015\pm 0.008,\\ {}\frac{\mathcal{B}\left({B}_s^0\to {K}_{\mathrm{S}}^0{K}^{+}{K}^{-}\right)}{\mathcal{B}\left({B}^0\to {K}_{\mathrm{S}}^0{\pi}^{+}{\pi}^{-}\right)}=0.0303\pm 0.0041\pm 0.0025\pm 0.0009,\\ {}\frac{\mathcal{B}\left({B}_s^0\to {K}_{\mathrm{S}}^0{K}^{\pm }{\pi}^{\mp}\right)}{\mathcal{B}\left({B}^0\to {K}_{\mathrm{S}}^0{\pi}^{+}{\pi}^{-}\right)}=1.818\pm 0.021\pm 0.031\pm 0.056,\end{array}\end{array}}$ B B 0 → K S 0 K + K − B B 0 → K S 0 π + π − = 0.578 ± 0.007 ± 0.017 , B B 0 → K S 0 K ± K ∓ B B 0 → K S 0 π + π − = 0.1363 ± 0.0035 ± 0.051 , B B s 0 → K S 0 π + π − B B 0 → K S 0 π + π − = 0.269 ± 0.011 ± 0.015 ± 0.008 , B B s 0 → K S 0 K + K − B B 0 → K S 0 π + π − = 0.0303 ± 0.0041 ± 0.0025 ± 0.0009 , B B s 0 → K S 0 K ± π ∓ B B 0 → K S 0 π + π − = 1.818 ± 0.021 ± 0.031 ± 0.056 , 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.