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arXiv · 0810.0987

NNLO corrections to B --> X_u l nu in the shape-function region

H. M. Asatrian·C. Greub·B. D. Pecjak
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Abstract

The inclusive decay B --> X_u l nu is of much interest because of its potential to constrain the CKM element |V_ub|. Experimental cuts required to suppress charm background restrict measurements of this decay to the shape-function region, where the hadronic final state carries a large energy but only a moderate invariant mass. In this kinematic region, the differential decay distributions satisfy a factorization formula of the form $H \cdot J \otimes S$, where S is the non-perturbative shape function, and the object $H \cdot J$ is a perturbatively calculable hard-scattering kernel. In this paper we present the calculation of the hard function H at next-to-next-to-leading order (NNLO) in perturbation theory. Combined with the known NNLO result for the jet function J, this completes the perturbative part of the NNLO calculation for this process.

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H. M. Asatrian, C. Greub, B. D. Pecjak. 2008-10-06. NNLO corrections to B --> X_u l nu in the shape-function region. https://doi.org/10.1103/physrevd.78.114028

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