Rescattering and chiral dynamics in B→ρπ decay

We examine the role of B⁰(B̄⁰)→σπ⁰→ π⁺ π^- π⁰ decay in the Dalitz plot analysis of B⁰(B̄⁰)→ρπ →π⁺π^-π⁰ decays, employed to extract the CKM parameter α. The σπ channel is significant because it can break the relationship between the penguin contributions in B→ρ⁰π⁰, B→ρ⁺π^-, and B→ρ^-π⁺ decays consequent to an assumption of isospin symmetry. Its presence thus mimics the effect of isospin violation. The σπ⁰ state is of definite CP, however; we demonstrate that the B→ρπ analysis can be generalized to include this channel without difficulty. The σ or f₀(400-1200) "meson" is a broad I = J = 0 enhancement driven by strong ππ rescattering; 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 →σπ and D→σπ analyses. We show that the use of this scalar form factor leads to an improved theoretical understanding of the measured ratio Br(B̄⁰→ρ^∓ π^±)/Br(B^-→ρ⁰ π^-).