Study of $B\to \Lambda\bar\Lambda K$ and $B\to \Lambda\bar\Lambda \pi$

We study three-body charmless baryonic B decays of $B \to \Lambda\bar\Lambda P$ with $P=\pi$ and $K$ in the standard model. We find that the branching ratios of the $K$ modes are about one order of magnitude larger than those of the corresponding $\pi$ modes unlike the cases of $B\to p\bar p P$. Explicitly, we obtain that $Br(B^-\to \Lambda\bar \Lambda K^-)=(2.8\pm 0.2)\times 10^{-6}$ and $Br(\bar B^0 \to\Lambda\bar \Lambda \bar K^0)=(2.5\pm 0.3)\times 10^{-6}$. The former agrees well with the BELLE experimental measurement of $(2.91^{+0.90}_{-0.70}\pm 0.38)\times 10^{-6}$, while the latter should be seen at the ongoing B factories soon.