Final state rescattering as a contribution toB→ργ

We provide a new estimate of the long-distance component to the radiative transition $B\to \rho \gamma$. Our mechanism involves the soft scattering of on-shell hadronic products of nonleptonic $B$ decay, as in the chain $B\to \rho \rho \to \rho \gamma$. We employ a phenomenological fit to scattering data to estimate the effect. The specific intermediate states considered here modify the $B\to \rho \gamma$ decay rate at roughly the $5-8\%$ 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 $B^0\to {\rho }^0\gamma$ channel and hence will provide an uncertainty in the extraction of $V_{\mathrm{td}}.$ This mechanism also affects the isospin relation between the rates for $B^{-}\to {\rho }^{-}\gamma$ and $B^0\to {\rho }^0\gamma$ and may generate $\mathrm{CP}$ asymmetries at experimentally observable levels.