Role of “intrinsic charm” in semileptonicB-meson decays

Abstract

We discuss the role of so-called ``intrinsic-charm'' operators in semileptonic $B$-meson decays, which appear first at order $1/{m}_{b}^{3}$ in the heavy quark expansion. We show by explicit calculation that---at scales $\ensuremath{\mu}\ensuremath{\le}{m}_{c}$---the contributions from ``intrinsic-charm'' effects can be absorbed into short-distance coefficient functions multiplying, for instance, the Darwin term. Then, the only remnant of ``intrinsic charm'' are logarithms of the form $\mathrm{ln}({m}_{c}^{2}/{m}_{b}^{2})$, which can be resummed by using renormalization-group techniques. As long as the dynamics at the charm-quark scale is perturbative, ${\ensuremath{\alpha}}_{s}({m}_{c})\ensuremath{\ll}1$, this implies that no additional nonperturbative matrix elements aside from the Darwin and the spin-orbit term have to be introduced at order $1/{m}_{b}^{3}$. Hence, no sources for additional hadronic uncertainties have to be taken into account. Similar arguments may be made for higher orders in the $1/{m}_{b}$ expansion.