Searches for $\Lambda^0_{b}$ and $\Xi^{0}_{b}$ decays to $K^0_{\rm S} p \pi^{-}$ and $K^0_{\rm S}p K^{-}$ final states with first observation of the $\Lambda^0_{b} \rightarrow K^0_{\rm S}p \pi^{-}$ decay

A search for previously unobserved decays of beauty baryons to the final states $K^0_{\rm\scriptscriptstyle S} p \pi^{-}$ and $K^0_{\rm\scriptscriptstyle S}p K^{-}$ is reported. The analysis is based on a data sample corresponding to an integrated luminosity of $1.0\,$fb$^{-1}$ of $pp$ collisions. The $\Lambda^0_{b} \rightarrow \overline{\kern -0.2em K}^0_{\rm\scriptscriptstyle S}p \pi^{-}$ decay is observed with a significance of $8.6\,\sigma$, with branching fraction \begin{eqnarray*} {\cal{B}}(\Lambda^0_{b} \rightarrow \overline{\kern -0.2em K}^0 p \pi^{-}) & = & \left( 1.26 \pm 0.19 \pm 0.09 \pm 0.34 \pm 0.05 \right) \times 10^{-5} \,, \end{eqnarray*} where the uncertainties are statistical, systematic, from the ratio of fragmentation fractions $f_{\Lambda}/f_{d}$, and from the branching fraction of the $B^0 \rightarrow K^0_{\rm\scriptscriptstyle S}\pi^{+}\pi^{-}$ normalisation channel, respectively. A first measurement is made of the $CP$ asymmetry, giving \begin{eqnarray*} A_{C\!P} (\Lambda^0_{b} \rightarrow \overline{\kern -0.2em K}^0 p \pi^{-}) & = & 0.22 \pm 0.13\mathrm{\,(stat)} \pm 0.03\mathrm{\,(syst)} \, . \end{eqnarray*} No significant signals are seen for $\Lambda^0_{b} \rightarrow K^0_{\rm\scriptscriptstyle S}p K^{-}$ decays, $\Xi^{0}_{b}$ decays to both the $K^0_{\rm\scriptscriptstyle S}p \pi^{-}$ and $K^0_{\rm\scriptscriptstyle S}p K^{-}$ final states, and the $\Lambda^0_{b} \rightarrow D^{-}_{s} (\rightarrow K^0_{\rm\scriptscriptstyle S} K^{-}) p$ decay, and upper limits on their branching fractions are reported.