Rescattering and chiral dynamics in B→ρπ decay -: art. no. 094004

We examine the role of B-0((B) over bar (0)) --> sigmapi(0) --> pi(+) pi(-) pi(0) decay in the Dalitz plot analysis of B-0((B) over bar (0)) --> rhopi --> pi(+) pi(-) pi(0) decays, employed to extract the CKM parameter alpha. The sigmapi channel is significant because it can break the relationship between the penguin contributions in B --> rho(0)pi(0), B --> rho(+)pi(-), and B --> rho(-)pi(+) decays consequent to an assumption of isospin symmetry. Its presence thus mimics the effect of isospin violation. The sigmapi(0) state is of definite CP, however; we demonstrate that the B --> rhopi analysis can be generalized to include this channel without difficulty. The sigma or f(0)(400-1200) "meson" is a broad I = J = 0 enhancement driven by strong pipi 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 --> sigmapi and D --> sigmapi analyses. We show that the use of this scalar form factor leads to an improved theoretical understanding of the measured ratio Br((B) over bar (0) -->rho(-/+) pi(+/-))/Br(B- -->rho(0)pi(-)).