Final state rescattering as a contribution to $B \to ργ$

Abstract

We provide a new estimate of the long-distance component to the radiative transition $B \to ργ$. Our mechanism involves the soft-scattering of on-shell hadronic products of nonleptonic $B$ decay, as in the chain $B \to ρρ\to ργ$. We employ a phenomenological fit to scattering data to estimate the effect. The specific intermediate states considered here modify the $B \to ργ$ decay rate at roughly the $5 \to 8%$ level, although the underlying effect has the potential to be larger. Contrary to other mechanisms of long distance physics which have been discussed in the literature, this yields a non-negligible modification of the $B^0 \to ρ^0 γ$ channel and hence will provide an uncertainty in the extraction of $V_{td}$. This mechanism also affects the isospin relation between the rates for $B^- \to ρ^-γ$ and $B^0 \to ρ^0 γ$ and may generate CP asymmetries at experimentally observable levels.