Feasibility of Extracting V_td from Radiative B(B_s) Decays

Abstract

We use existing measurements of $D^-\to K^{\ast0}\rho^-$ and $B\to \psi+K^\ast$, coupled with flavor independence of QCD, and with vector meson dominance to show that long distance contributions to $B\to \rho +\gamma$ are potentially very serious. We note that long distance (LD) contributions can be appreciably different in $B^-\to \rho^-+\gamma$ and $B^0\to \rho^0 (\omega) +\gamma$. 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 $B^-\to \rho^-+\gamma$, $B^0\to \rho^0 (\omega) +\gamma$, along with $B\to K^\ast +\gamma$ appear necessary for a meaningful extraction of \vtd. Measurements of $B_S\to \phi+\gamma$ and $K^{\ast0}+\gamma$ could also provide very useful consistency checks.