From $Ξ_b \to Λ_b π$ to $Ξ_c \to Λ_c π$

Using a successful framework for describing S-wave hadronic decays of light hyperons induced by a subprocess $s \to u (\bar u d)$, we presented recently a model-independent calculation of the amplitude and branching ratio for $Ξ^-_b \to Λ_b π^-$ in agreement with a LHCb measurement. The same quark process contributes to $Ξ^0_c \to Λ_c π^-$, while a second term from the subprocess $cs \to cd$ has been related by Voloshin to differences among total decay rates of charmed baryons. We calculate this term and find it to have a magnitude approximately equal to the $s \to u (\bar u d)$ term. We argue for a negligible relative phase between these two contributions, potentially due to final state interactions. However, we do not know whether they interfere destructively or constructively. For constructive interference one predicts ${\cal B}(Ξ_c^0 \to Λ_c π^-) = (1.94 \pm 0.70)\times 10^{-3}$ and ${\cal B}(Ξ_c^+ \to Λ_c π^0) = (3.86 \pm 1.35)\times 10^{-3}$. For destructive interference, the respective branching fractions are expected to be less than about $10^{-4}$ and $2 \times 10^{-4}$.

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