Vector Dominance Effects in Weak Radiative Decays of the B Mesons

Abstract

The long distance vector-meson-dominance (VMD) effects on the weak radiative decays $\bb\toργ$ and $\bb^0\to D^{*0}γ$ are studied. For $\bb\toργ$ decays, the VMD contribution is $(10-20)\%$ of the short-distance penguin amplitude. The pole effect is as important as the VMD one in the decay $B^-\toρ^-γ$, but it is suppressed in $\bb^0\to ρ^0γ$. The branching ratio of $\bb\toργ$, estimated to be of order $10^{-6}$, strongly depends on the sign of the Wolfenstein parameter $ρ$. A measurement of any deviation of the ratio $R=Γ(B^-\toρ^- γ)/Γ(\bb^0\toρ^0γ)$ away from the isospin value 2 will not only provide a probe on the long-range contribution but also fix the sign of $ρ$: $R>2$ for $ρ<0$ and $R<2$ for $ρ>0$. The decay $\bb^0\to D^{*0}γ$ 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.