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A search for charmless three-body decays of $B^0$ and $B_{s}^0$ mesons with a$K_{\rm S}^0$ meson in the final state is performed using the $pp$ collisiondata, corresponding to an integrated luminosity of $1.0\,\mbox{fb}^{-1}$,collected at a centre-of-mass energy of $7\mathrm{\,Te\kern -0.1em V}$ recordedby the LHCb experiment. Branching fractions of the $B_{(s)}^0 \to K_{\rm S}^0h^{+} h^{\prime -}$ decay modes ($h^{(\prime)} = \pi, K$), relative to the wellmeasured $B^0 \to K_{\rm S}^0 \pi^{+} \pi^{-}$ decay, are obtained. Firstobservation of the decay modes $B_s^0 \to K_{\rm S}^0 K^{\pm} \pi^{\mp}$ and$B_s^0 \to K_{\rm S}^0 \pi^{+} \pi^{-}$ and confirmation of the decay $B^0 \toK_{\rm S}^0 K^{\pm} \pi^{\mp}$ are reported. The following relative branchingfraction 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_{\rmS}^0 \pi^{+} \pi^{-})} &=& 0.128 \pm 0.017 \, ({\rm stat.}) \pm 0.009 \, ({\rmsyst.}) \,, \\ \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 \, ({\rmstat.}) \pm 0.023 \, ({\rm syst.}) \,, \\ \nonumber \frac{{\cal B}(B_s^0 \toK_{\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 \toK_{\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 \toK_{\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*}

the journal of high energy physics/the journal of high energy physics

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 $B_{s}^0  \to K_{\rm S}^0 \pi^{+} \pi^{-}$