QCD-Based Interpretation of the Lepton Spectrum in Inclusive $\bar{B}\to X_u\ell \bar{\nu }$ Decays

Abstract

We present a QCD-based approach to the endpoint region of the lepton spectrum in $\bar{B}\to X_u\ell \bar{\nu }$ decays. We introduce a genuinely nonperturbative form factor, the shape function, which describes the fall-off of the spectrum close to the endpoint. The moments of this function are related to forward scattering matrix elements of local, higher-dimension operators. We find that nonperturbative effects are dominant over a finite region in the lepton energy spectrum, the width of which is related to the kinetic energy of the $b$-quark inside the $B$ meson. Applications of our method to the extraction of fundamental standard model parameters, among them $V_{ub}$, are discussed in detail.

Comments: 17 pages LaTeX, 3 post- script figures available upon request, CERN-TH.7087/93