Matching of the Shape Function

Details Matching of the Shape Function Matching of the Shape Function

1999-07-26

arxiv.org/abs/hep-ph/9907501v3

Phys.Lett.B466:313,1999

Physics

High Energy Physics

High Energy Physics - Phenomenology

11 pages, 1 figure added, minor changes in the text

Scientific paper

10.1016/S0370-2693(99)01103-X

The shape function f(k_+) describes Fermi motion effects in inclusive semi-leptonic decays such as B -> X_u+e+nu near the end-point of the lepton spectrum. We compute the leading one-loop corrections to the shape function f(k_+) in the effective theory with a hard cut-off regularization. The matching constant onto full QCD is infrared safe, i.e. the leading infrared singularity represented by the term log^2(k_+) cancels in the difference of integrals. We compare the hard cut-off result with the result in dimensional regularization, the latter containing an additional factor of two in the coefficient of the log^2(k_+) term, and consequently requiring an oversubtraction.

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