Progress in computing inclusive B decay spectra

We review the progress in the QCD calculation of inclusive decay spectra. It was recently shown that the inherent infrared finiteness of inclusive spectra extends beyond the level of logarithms. Dressed Gluon Exponentiation makes practical use of this property by computing the Sudakov exponent as a Borel sum. Based on renormalon analysis, infrared sensitivity in the exponent is reflected in power corrections that are inversely proportional to the third power of the mass. Therefore, the parametric enhancement of non-perturbative corrections near the phase–space boundary is effective only in a small region. Consequently, the on-shell decay spectrum provides a good approximation to the meson decay. In particular, it facilitates a precise determination of |Vub| from present measurements of inclusive charmless semileptonic widths without involving a non-perturbative “shape function”.