Vector Dominance Effects in Weak Radiative Decays of the B Mesons

The long distance vector-meson-dominance (VMD) effects on the weak radiative decays $\text{bb}\to \rho \gamma$ and ${\text{bb}}^0\to D^{\ast 0}\gamma$ are studied. For $\text{bb}\to \rho \gamma$ decays, the VMD contribution is $(10-20)\mathrm{\%}$ of the short-distance penguin amplitude. The pole effect is as important as the VMD one in the decay $B^{-}\to {\rho }^{-}\gamma$, but it is suppressed in $\bb^0\to \rho^0\gamma$\mathrm{.}Thebranchingratioof$\bb\to\rho\gamma$, estimated to be of order ${10}^{-6}$, strongly depends on the sign of the Wolfenstein parameter $\rho$. A measurement of any deviation of the ratio $R=\Gamma(B^-\to\rho^- \gamma)/\Gamma(\bb^0\to\rho^0\gamma)$ away from the isospin value 2 will not only provide a probe on the long-range contribution but also fix the sign of $\rho$: $R>2$ for $\rho <0$ and $R<2$ for $\rho >0$. The decay $\bb^0\to D^{*0}\gamma$ does not receive short-distance contributions, and its branching ratio, predicted to be $0.9\times {10}^{-6}$, is dominated by $W$-exchange accompanied by a photon emission.