Selection rules in three-body B decay from factorization

Abstract

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^0-->D^0-bar\pi^+\pi^-, practically no events should be found in the corner of E(\pi^+) < \Lambda_{QCD} as compared with the corner of E(\pi^-) < \Lambda_{QCD}. We also predict that there should be very few three-body decay events with a 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^0 -->D^0-bar\pi^+\pi^-, the latter predicts that the decay matrix element vanishes in the zero-four-momentum limit of \pi^+ instead of \pi^-. Since this marked difference from the soft pion theorem is directly related to the issue of short-distance QCD dominance in the FSI of two-body B decays, experimental test of the selection rules will shed light on strong interaction dynamics of B decay.