Radiative corrections and enhanced power corrections for the shape function in inclusive B decays ⁎

In the heavy-quark limit, the decay spectrum for radiative and semileptonic inclusive B-meson decays are described by a structure function, i.e. the shape function. We study the operator structure of the shape function, taking into account the QCD radiative corrections. Separating the singular short-distance behavior due to the one-loop cusp divergence in a systematic way, the long-distance degrees of freedom in the shape function are disentangled based on the QCD equations of motion and heavy-quark symmetry, as the quark-gluon correlations relevant for the (enhanced) power corrections for the decay rates.