Prediction of Three-body $B^0\to {\rho }^{-}p\bar{n},{\pi }^{-}p\bar{n}$ Decay Rates

We predict the rates of the charmless three-body $B^0\to {\rho }^{-}p\bar{n}$ and ${\pi }^{-}p\bar{n}$ modes due to weak vector current contributions to be $\sim 4\times 10^{-6}$and$2\times 10^{-6}$, respectively. The basis is a factorization approach of current produced nucleon pairs, together with an isospin transformation that relates nucleon weak vector form factors to electromagnetic form factors. Adding the axial vector current contribution, we find $B^0\to {\rho }^{-}p\bar{n}$ and $B^{+}\to {\rho }^{0}p\bar{n}$ to be at ${10}^{-5}$ order. The three-body modes appear to dominate over the two-body modes such as $B\to p\bar{p}$, $p\bar{\mathrm{\Lambda }}$.