Shape Functions from B̄ → X c l ν̄ l

We study inclusive semi-leptonic ¯ B → X c ℓ¯ ν 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 SCET to describe massive collinear quarks. Working at tree level and including O(Λ QCD /m b) power corrections, we show that the decay rate 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.