Searches for $\Lambda_{b}^{0}$ and $\Xi_{b}^{0}$ decays to $K_{\mathrm S}^{0}p\pi^{-}$ and $K_{\mathrm S}^{0}pK^{-}$ final states with the first observation of the $\Lambda_{b}^{0} \to K_{S}^{0}p\pi^{-}$ decay

A search for previously unobserved decays of beauty baryons to the final states $K^0_{\mathrm{S}}p\pi^-$ and $K^0_{\mathrm{S}}pK^-$ is reported. The analysis is based on a data sample corresponding to an integrated luminosity of $1.0\,\mathrm{fb}^{-1}$ of $pp$ collisions. The $\Lambda^0_b \rightarrow K^0_{\mathrm{S}}p\pi^-$ decay is observed for the first time with a significance of $8.6\,\sigma$, and a measurement is made of the $CP$ asymmetry, which is consistent with zero. No significant signals are seen for $\Lambda^0_b \rightarrow K^0_{\mathrm{S}}pK^-$ decays, $\Xi^0_b$ decays to both $K^0_{\mathrm{S}}p\pi^-$ and $K^0_{\mathrm{S}}pK^-$ final states, and the $\Lambda^0_b \rightarrow D^-_s (K^0_{\mathrm{S}}K^-)p$ decay, and upper limits on their branching fractions are reported.