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

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 $3f{b}^{-1}$. The branching fractions are measured relative to that of the $B^0 \to K_{$\mathrm{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 ; $(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})$; \pm 0.015 ; $(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})$,, \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 ; $(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})$; \pm 0.033 ; $(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})$,, \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 ; $(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})$; \pm 0.031 ; $(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})$; \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} ; $(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})$ ; \pm 0.11\phantom{0} ; $(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})$; \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 $f_s\mathrm{/}{f}_d$ represents the ratio of hadronisation fractions of the $B_s^0$ and $B^0$ mesons.