A search for previously unobserved decays of beauty baryons to the final states $K^0_{rmscriptscriptstyle S} p pi^{-}$ and $K^0_{rmscriptscriptstyle S}p K^{-}$ is reported. The analysis is based on a data sample corresponding to an integrated luminosity of $1.0,$fb$^{-1}$ of $pp$ collisions. The $Lambda^0_{b} rightarrow overline{kern -0.2em K}^0_{rmscriptscriptstyle S}p pi^{-}$ 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 $B^0 rightarrow K^0_{rmscriptscriptstyle S}pi^{+}pi^{-}$ 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 0.13mathrm{,(stat)} pm 0.03mathrm{,(syst)} , . end{eqnarray*} No significant signals are seen for $Lambda^0_{b} rightarrow K^0_{rmscriptscriptstyle S}p K^{-}$ decays, $Xi^{0}_{b}$ decays to both the $K^0_{rmscriptscriptstyle S}p pi^{-}$ and $K^0_{rmscriptscriptstyle S}p K^{-}$ final states, and the $Lambda^0_{b} rightarrow D^{-}_{s} (rightarrow K^0_{rmscriptscriptstyle S} K^{-}) p$ decay, and upper limits on their branching fractions are reported.
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