Semileptonic and Exclusive Rare B Decays

The exclusive rare decay $B \ra K^\ast \gamma$ takes place in a region of maximum recoil, $q^{2}=0$, posing a problem for nonrelativistic quark models which are usually thought to be most reliable at zero recoil. The Bauer--Stech--Wirbel (BSW) model, formulated in the infinite--momentum--frame (IMF) formalism, is designed to work at $q^2=0$. We show in this model that the ratio relating the decay $B \ra K^\ast \gamma$ and the $q^2$--spectrum of the semileptonic decay $B\ra \rho e {\bar \nu}$, becomes independent of the wave function in the SU(3) flavor symmetry limit. We show that this feature is also true in relativistic quark models formulated in the IMF or light--cone formalism, if the $b$ quark is infinitely heavy. In fact, these relativistic models, which have a different spin structure from the BSW case, reduce to the BSW model in the heavy $b$--quark limit. A direct measurement of the $q^2$--spectrum of the semileptonic decay can therefore provide accurate information for the exclusive rare decay.