Rare $B$-Decays and Heavy to Light Semileptonic Transitions in the Isgur and Wise Limit

Abstract

From the experimental branching ratios for $B^- --> \rho^0 l^-\bar\nu_l$ and $D^+ --> {\overl K}^{*0}({\overl K}^0) e^+ \nu_e$ one finds, in the Heavy Quark Limit of $HQET$, $ |V_{bu}|=(8.1\pm 1.7) x 10^{-3}$, larger but consistent with the actual quoted range $(2 - 7) x 10^{-3}$. In the same framework one predicts for $R(B --> K^*\gamma)=( 2 \pm 2 ) 10^{-2}$.