Two-loop relations for heavy-quark parameters in the shape-function scheme

Moments of the renormalized B-meson shape function provide a natural way to define short-distance, running heavy-quark parameters such as the b-quark mass and kinetic energy. These parameters are particularly well suited for studies of inclusive decay distributions. The definitions of mb and μπ2 in this “shape-function scheme” are derived to two-loop order. Using previous determinations of heavy-quark parameters in other schemes, we find mb(μf)=(4.63±0.08) GeV and μπ2(μf)=(0.15±0.07) GeV2 at a reference scale μf=1.5 GeV.