Study of $ B_{(s)}^0\to K_{\mathrm{S}}^0{h^{+}}{h^{{\prime -}}} $ decays with first observation of $ B_s^0\to K_{\mathrm{S}}^0{K^{\pm }}{\pi^{\mp }} $ and $ B_s^0\to K_{\mathrm{S}}^0{\pi^{+}}{\pi^{-}} $

Abstract A search for charmless three-body decays of B 0 and $ B_s^0 $ mesons with a $ K_{\mathrm{S}}^0 $ meson in the final state is performed using the pp collision data, corresponding to an integrated luminosity of 1.0 fb−1, collected at a centre-of-mass energy of 7 TeV recorded by the LHCb experiment. Branching fractions of the $ B_{(s)}^0\to K_{\mathrm{S}}^0{h^{+}}{h^{{\prime -}}} $ decay modes (h (′) = π, K), relative to the well measured $ {B^0}\to K_{\mathrm{S}}^0{\pi^{+}}{\pi^{-}} $ decay, are obtained. First observation of the decay modes $ B_s^0\to K_{\mathrm{S}}^0{K^{\pm }}{\pi^{\mp }} $ and $ B_s^0\to K_{\mathrm{S}}^0{\pi^{+}}{\pi^{-}} $ and confirmation of the decay $ {B^0}\to K_{\mathrm{S}}^0{K^{\pm }}{\pi^{\mp }} $ are reported. The following relative branching fraction measurements or limits are obtained $ \begin{array}{*{20}{c}} {\frac{{\mathcal{B}\left( {{B^0}\to K_{\mathrm{S}}^0{K^{\pm }}{\pi^{\mp }}} \right)}}{{\mathcal{B}\left( {{B^0}\to K_{\mathrm{S}}^0{\pi^{+}}{\pi^{-}}} \right)}}=0.128\pm 0.017\left( {\mathrm{stat}.} \right)\pm 0.009\left( {\mathrm{syst}.} \right),} \hfill \\ {\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)}}=0.385\pm 0.031\left( {\mathrm{stat}.} \right)\pm 0.023\left( {\mathrm{syst}.} \right),} \hfill \\ {\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)}}=0.29\pm 0.06\left( {\mathrm{stat}.} \right)\pm 0.03\left( {\mathrm{syst}.} \right)\pm 0.02\left( {{{{{f_s}}} \left/ {{{f_d}}} \right.}} \right),} \hfill \\ {\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)}}=1.48\pm 0.12\left( {\mathrm{stat}.} \right)\pm 0.08\left( {\mathrm{syst}.} \right)\pm 0.12\left( {{{{{f_s}}} \left/ {{{f_d}}} \right.}} \right)} \hfill \\ {\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)}}\in \left[ {0.004;0.068} \right]\;\mathrm{at}\;90\%\;\mathrm{CL}.} \hfill \\ \end{array} $