Relationship between form factors in Semileptonic B¯ and D decays and exclusive rare B¯-meson decays

Abstract

We show that existing data on the semileptonic decays $D\to K{e}^{+}{\nu }_e$ and $D\to K^{*}{e}^{+}{\nu }_e$ provide information on matrix elements relevant for the rare $\overline{B}$-meson decays $\overline{B}\to K{e}^{+}{e}^{-}$, $\overline{B}\to K^{*}{e}^{+}{e}^{-}$, and $\overline{B}\to K^{*}\gamma$ and that future data on $\overline{B}\to \rho e{\overline{\nu }}_e$ and $\overline{B}\to \pi e{\overline{\nu }}_e$ will further constrain them. A discussion of how the form factors for these latter decays are in turn determined by semileptonic $D$ decays at the corresponding recoil momenta is also presented.