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On the smallness of Tree-dominated Charmless Two-body Baryonic $B$ Decay Rates

The long awaited baryonic $B$ decay $\bar B{}^0\to p\bar p$ was recently observed by LHCb with a branching fraction of order $10^{-8}$. All the earlier model predictions are too large compared with experiment. In this work, we point out that for a given tree operator $O_i$, the contribution from its Fiertz transformed operator, an effect often missed in the literature, tends to cancel the internal $W$-emission amplitude induced from $O_i$. The wave function of low-lying baryons are symmetric in momenta and the quark flavor with the same chirality, but antisymmetric in color indices. Using these symmetry properties and the chiral structure of weak interactions, we find that half of the Feynman diagrams responsible for internal $W$-emission cancel. Since this feature holds in the charmless modes but not in the charmful ones, we advocate that the partial cancellation accounts for the smallness of the tree-dominated charmless two-body baryonic $B$ decays. This also explains why most previous model calculations predicted too large rates as the above consideration was not taken into account. Finally, we emphasize that, contrary to the claim in the literature, the internal $W$-emission tree amplitude should be proportional to the Wilson coefficient $c_1+c_2$ rather than $c_1-c_2$.