Shape functions from B¯→Xcℓν¯ℓ

We study inclusive semileptonic B¯→X_cℓν¯_ℓ decay using the power counting m_c∼Λ_QCD√(m_b). Assuming this scaling for the charm-quark mass, the decay kinematics can be chosen to access the shape-function region even in b→c transitions. To apply effective field theory methods in this region we extend soft-collinear effective theory to describe massive collinear quarks. We calculate the tree-level decay rate, including O(Λ_QCD/m_b) power corrections, and show that it factorizes into a convolution of jet and shape functions. We identify a certain kinematical variable whose decay spectrum is proportional to the universal leading-order shape function familiar from b→u decay, and speculate as to whether information about this shape function can be extracted from data on b→c decay.