Study of $B\to \mathrm{\Lambda }\bar{\mathrm{\Lambda }}K$ and $B\to \mathrm{\Lambda }\bar{\mathrm{\Lambda }}\pi$

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 $Br(B^{-}\to \mathrm{\Lambda }\bar{\mathrm{\Lambda }}{K}^{-})=(2.8\pm 0.2)\times {10}^{-6}$ and $Br({\bar{B}}^0\to \mathrm{\Lambda }\bar{\mathrm{\Lambda }}{\bar{K}}^0)=(2.5\pm 0.3)\times {10}^{-6}$. The former agrees well with the BELLE experimental measurement of $(2.91_{-0.70}^{+0.90}\pm 0.38)\times {10}^{-6}$, while the latter should be seen at the ongoing B factories soon.