Heavy quark distribution function in QCD and the AC 2M 2 model

Abstract

We show the phenomenological AC 2M 2 ansatz to be consistent with QCD through order 1/ m b in the description of B → l v l + X u and B → γ + X s transitions, including their energy spectra and differential distributions. This suggests a concrete realization of the QCD distribution function, which we call the “Roman” function. Yet the AC 2M 2 description of the end-point domain in B → l v l + X c is, formally speaking, incompatible with QCD: a different distribution function enters the description of b → c decays as compared to the transitions to massless quarks. The intrinsic limitation of the AC 2M 2 model could reveal itself in different values of the effective b quark mass from fits of the Λ b and B decays.