Models of semileptonic b → u decay

In this paper, the author discusses some theoretical issues of models for the b → u semileptonic transition. There are two ways to calculate rates in b → u semileptonic decay. One method performs the calculation of the decay of a b-quark into an up-quark plus ev, with the decay being independent of the spectator quark in the B-meson. The other technique calculates bound-state transitions to individual resonances B → Mev, where M = π, ρ, A1,... There are also two methods for the experimental detections of b → uev decays. One looks in the inclusive electron energy distribution above the energy at which b→ cev decays can no longer be produced (i.e., above Ee = 2.4 GeV). Any electrons (above background) with energies in this endpoint region are due to b → u transitions. A second method looks for exclusive B → Mev decays where again M = π, ρ, A1... One of the points of this paper is that only models that provide a complete calculation of the electron distribution (such as the quark-decay model or the hybrid model described later) should be applied to the inclusive electron-distribution measurements. The bound-state models should be reserved for the processes that they explicitly calculate, which are the exclusive decay modes. This ideal is not present practice. The electron spectrum from the calculations of B → πev and B → ρev are frequently applied to the endpoint electron distributions to bound the KM angles as if these modes were the full decay rate