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arXiv · hep-ph/9907501

Matching of the Shape Function

U. Aglietti·G. Ricciardi
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Abstract

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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U. Aglietti, G. Ricciardi. 1999-09-21. Matching of the Shape Function. https://doi.org/10.1016/s0370-2693(99)01103-x

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