Semileptonic and Exclusive Rare B Decays

The exclusive rare decay B → Kγ takes place in a region of maximum recoil, q = 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 = 0. We show in this model that the ratio relating the decay B → Kγ and the q–spectrum of the semileptonic decay B → ρeν̄, 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–spectrum of the semileptonic decay can therefore provide accurate information for the exclusive rare decay.