Feasibility of Extracting Vtd from Radiative B(Bs) Decays

We use experimental information on D^-→K*⁰ρ^- and B→ψ+K*, coupled with flavor independence of QCD, and with vector meson dominance, to show that long distance (LD) contributions to B→ρ+γ, especially to B^-→ρ^-+γ, are potentially very serious. Estimates based on the annihilation graph are shown to lead to similar conclusions. We emphasize that LD contributions can be appreciably different in B^-→ρ^-+γ and B⁰→ρ⁰(ω)+γ. All radiative decays of B, B_s are shown to be governed essentially by two LD and two short distance (SD) hadronic entities. Despite the presence of considerable LD contributions, we show how separate measurements of B^-→ρ^-+γ, B⁰→ρ⁰(ω)+γ, along with B→K*+γ, can be used for a systematic extraction of V_td. Measurements of B_s→ɸ+γ and K*⁰+γ could also provide very useful consistency checks.