From ${\Xi }_b\to {\Lambda }_b\pi$ to ${\Xi }_c\to {\Lambda }_c\pi$

Abstract

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 ${\Xi }_b^{-}\to {\Lambda }_b{\pi }^{-}$ in agreement with a LHCb measurement. The same quark process contributes to ${\Xi }_c^0\to {\Lambda }_c{\pi }^{-}$, 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 $\mathcal{B}({\Xi }_c^0\to {\Lambda }_c{\pi }^{-})=(1.94\pm 0.70)\times 10^{-3}$ and $\mathcal{B}({\Xi }_c^{+}\to {\Lambda }_c{\pi }^0)=(3.86\pm 1.35)\times 10^{-3}$. For destructive interference, the respective branching fractions are expected to be less than about $10^{-4}$ and $2\times 10^{-4}$.

Comments: To be published in Physics Letters B