Selection rules in three-body B decay from factorization

Extending the dynamics underlying the factorization calculation of two-body decays, we propose simple selection rules for nonresonant three-body B decays. We predict, for instance, that in the Dalitz plot of B → D0π+π−, practically no events should be found in the corner region of E(π) ≤ ΛQCD as compared with the corner of E(π−) ≤ ΛQCD. We also predict that there should be very few three-body decay events containing one soft meson resonance and two energetic mesons or meson resonances. The selection rules are quite different from the soft-pion theorem, since they apply to different kinematical regions. For B → D0π+π−, the latter predicts that the decay matrix element vanishes in the zero four-momentum limit of π− instead of π. Since this marked difference from the soft-pion theorem is directly related to the issue of short-distance QCD dominance in two-body B decays, experimental test of the selection rules will shed light on strong interaction dynamics of B decay. PACS number(s) 13.20.He, 12.38.-t, 11.30.Rd, 11.30.-q Typeset using REVTEX