Prediction of Three-body B⁰→ ρ-pn, π-pn Decay Rates

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We predict the rates of the charmless three-body B⁰→ ρ-pn and π-pn modes due to weak vector current contributions to be 4× 10⁻⁶ and 2× 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 B⁰→ ρ-pn and B+→ ρ⁰pn to be at 10⁻⁵ order. The three-body modes appear to dominate over the two-body modes such as B→ pp, p Λ.