QCD-based interpretation of the lepton spectrum in inclusiveB¯→Xuℓν¯decays

We present a QCD-based approach to the end-point region of the lepton spectrum in $\overline{B}\to X_u\ell \overline{\nu }$ decays. A genuinely nonperturbative form factor, the shape function, describes the falloff of the spectrum close to the end point. 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. In this region, a resummation of the most singular terms in the operator product expansion is performed. Applications of our method to the extraction of fundamental standard model parameters, among them $V_{\mathrm{ub}}$, are discussed.