Rescattering and chiral dynamics in B\to ρπdecay

Abstract

We examine the role of B^0(\bar B^0) \to σπ^0 \to π^+π^- π^0 decay in the Dalitz plot analysis of B^0 (\bar B^0) \to ρπ\to π^+π^-π^0 decays, employed to extract the CKM parameter α. The σπchannel is significant because it can break the relationship between the penguin contributions in B\toρ^0π^0, B\toρ^+π^-, and B\toρ^-π^+ decays consequent to an assumption of isospin symmetry. Its presence thus mimics the effect of isospin violation. The σπ^0 state is of definite CP, however; we demonstrate that the B\toρπanalysis can be generalized to include this channel without difficulty. The σor f_0(400-1200) ``meson'' is a broad I=J=0 enhancement driven by strong ππrescattering; a suitable scalar form factor is constrained by the chiral dynamics of low-energy hadron-hadron interactions - it is rather different from the relativistic Breit-Wigner form adopted in earlier B\toσπand D\toσπanalyses. We show that the use of this scalar form factor leads to an improved theoretical understanding of the measured ratio Br(\bar B^0 \to ρ^\mp π^\pm) / Br(B^-\to ρ^0 π^-).