Feasibility of Extracting V_td from Radiative B(B_s) Decays

We use existing measurements of $D^-\to K^{\ast0}ρ^-$ and $B\to ψ+K^\ast$, coupled with flavor independence of QCD, and with vector meson dominance to show that long distance contributions to $B\to ρ+γ$ are potentially very serious. We note that long distance (LD) contributions can be appreciably different in $B^-\to ρ^-+γ$ and $B^0\to ρ^0 (ω) +γ$. All radiative decays of $B$, $B_S$ are shown to be governed essentially by two LD and two short-distance (SD) hadronic entities. Separate measurements of $B^-\to ρ^-+γ$, $B^0\to ρ^0 (ω) +γ$, along with $B\to K^\ast +γ$ appear necessary for a meaningful extraction of \vtd. Measurements of $B_S\to ϕ+γ$ and $K^{\ast0}+γ$ could also provide very useful consistency checks.

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