Updated branching fraction measurements of $B^0_{(s)} \to K_{\mathrm{\scriptscriptstyle S}}^0 h^+ h^{\prime -}$ decays

Abstract: The charmless three-body decays $B^0_{(s)} \to K_{\mathrm{\scriptscriptstyle S}}^0 h^+ h^{\prime -}$ (where $h^{(\prime)} = \pi, K$) are analysed using a sample of $pp$ collision data recorded by the LHCb experiment, corresponding to an integrated luminosity of $3\mbox{fb}^{-1}$. The branching fractions are measured relative to that of the $B^0 \to K_{\mathrm{\scriptscriptstyle S}}^0 \pi^{+} \pi^{-}$ decay, and are determined to be: \begin{eqnarray*} \frac{{\cal B}(B^0\rightarrow K^0_{\rm S}K^{\pm}\pi^{\mp})}{{\cal B}(B^0\rightarrow K^0_{\rm S}\pi^{+}\pi^{-})} = {} & 0.123 \pm 0.009 \; \mathrm{\,(stat)}\; \pm 0.015 \; \mathrm{\,(syst)}\,, \frac{{\cal B}(B^0\rightarrow K^0_{\rm S}K^{+}K^{-})} {{\cal B}(B^0\rightarrow K^0_{\rm S}\pi^{+}\pi^{-})} = {} & 0.549 \pm 0.018 \; \mathrm{\,(stat)}\; \pm 0.033 \; \mathrm{\,(syst)}\,, \frac{{\cal B}(B_{s}^0\rightarrow K^0_{\rm S}\pi^{+}\pi^{-})}{{\cal B}(B^0\rightarrow K^0_{\rm S}\pi^{+}\pi^{-})} = {} & 0.191 \pm 0.027 \; \mathrm{\,(stat)}\; \pm 0.031 \; \mathrm{\,(syst)}\; \pm 0.011 \; (f_s/f_d) \,, \frac{{\cal B}(B_{s}^0\rightarrow K^0_{\rm S}K^{\pm}\pi^{\mp})} {{\cal B}(B^0\rightarrow K^0_{\rm S}\pi^{+}\pi^{-})} = {} & 1.70\phantom{0} \pm 0.07\phantom{0} \; \mathrm{\,(stat)} \; \pm 0.11\phantom{0} \; \mathrm{\,(syst)}\; \pm 0.10\phantom{0} \; (f_s/f_d) \,, \frac{{\cal B}(B_{s}^0\rightarrow K^0_{\rm S}K^{+}K^{-})}{{\cal B}(B^0\rightarrow K^0_{\rm S}\pi^{+}\pi^{-})} \in {} & [0.008 - 0.051] \rm ~at~90\%~confidence~level, \end{eqnarray*} where $f_s/f_d$ represents the ratio of hadronisation fractions of the $B^0_s$ and $B^0$ mesons.