Three-body charmless baryonic $\bar B^0_s$ decays

We study for the first time the three-body charmless baryonic decays $\bar B^0_s\to \bar p \Lambda M^+ (p \bar \Lambda M^-)$, with $M=\pi, K$. We find that the branching ratios of $\bar B^0_s\to (\bar p \Lambda K^+$ and $p\bar \Lambda K^-)$ and $\bar B^0_s\to p\bar \Lambda \pi^-$ are $(5.1\pm 1.1)\times 10^{-6}$ and $(2.8\pm 1.5)\times 10^{-7}$, respectively, which agree with recent experimental results reported by the LHCb collaboration. In addition, we derive the relations \mbox{${\cal B}(\bar B^0_s\to \bar p \Lambda K^+)\simeq (f_K/f_\pi)^2(\tau_{B^0_s}/\tau_{B^0}) {\cal B}(\bar B^0\to \bar p \Lambda \pi^+)$} and ${\cal B}(\bar B^0_s\to p\bar \Lambda \pi^-)/{\cal B}(\bar B^0_s\to p\bar \Lambda K^-)\simeq {\cal B}(B^-\to p\bar p \pi^-)/{\cal B}(B^-\to p\bar p K^-)$ to be confronted to future experimental measurements. The fact that all four processes $B^0_s, \bar B^0_s \to p\bar \Lambda K^-, \bar p \Lambda K^+$ can occur opens the possibility of decay-time-dependent CP violation measurements in baryonic $B$ decays, something that had not been realised before.