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

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

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

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

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Study of B(s)0→KS0h+h′−B(s)0​→KS0​h+h′− decays with first observation of Bs0→KS0K±π∓Bs0​→KS0​K±π∓ and Bs0→KS0π+π−Bs0​→KS0​π+π−

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Study of B(s)0→KS0h+h′−B(s)0​→KS0​h+h′− decays with first observation of Bs0→KS0K±π∓Bs0​→KS0​K±π∓ and Bs0→KS0π+π−Bs0​→KS0​π+π−

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

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

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