Unravelling soft components in the shape function for inclusive B decays

In the heavy-quark limit, the decay spectrum in radiative and semileptonic inclusive B-meson decays is determined by a universal structure function, i.e. the shape function. We study the constraints on the bilocal heavy-quark operator for the shape function from the QCD equations of motion and heavy-quark symmetry, and obtain a new basis of nonlocal operators that reveal relevant soft components in the shape function. Those nonlocal operators represent the “kinetic energy distribution” of the bquark inside the B-meson and the four-parton correlations with additional quarks and gluons. A corresponding local operator basis relevant for relating the shape function to HQET parameters is also given, and novel effects of the quark-gluon correlations are discussed. ∗) E-mail: [email protected] ∗∗) E-mail: [email protected] ∗∗∗) E-mail: [email protected] 1 typeset using PTPTEX.cls 〈Ver.0.9〉