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Shape Functions from B -> X_c \ell ν

H. Boos·Th. Feldmann·T. Mannel·B. D. Pecjak
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Abstract

We study inclusive semi-leptonic (B -> X_c \ell ν) decay using the power counting m_c ~ \sqrt{Lambda_{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. We calculate the tree-level decay rate, including O(Lambda_{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.

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H. Boos, Th. Feldmann, T. Mannel, B. D. Pecjak. 2006-01-30. Shape Functions from B -> X_c \ell ν. https://doi.org/10.1103/physrevd.73.036003

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