Feasibility of Extracting V_td from Radiative B(B_s) Decays

Abstract

We use existing measurements of $D^{-}\to K^{\ast 0}{\rho }^{-}$ 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 $B_S\to \varphi +\gamma$ and $K^{\ast 0}+\gamma$ could also provide very useful consistency checks.

19 pages. [Figures can be obtained by sending e-mail message to [email protected]]

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