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Shape-function effects and split matching in
Phys. Rev. D 74, 014005 – Published 7 July, 2006
DOI: https://doi.org/10.1103/PhysRevD.74.014005
Abstract
We derive the triply differential spectrum for the inclusive rare decay in the shape-function region, in which is jetlike with . Experimental cuts make this a relevant region. The perturbative and nonperturbative parts of the matrix elements can be defined with the soft-collinear effective theory, which is used to incorporate corrections consistently. We prove that, with a suitable power counting for the dilepton invariant mass, the same universal jet and shape functions appear as in and decays. Parts of the usual corrections go into the jet function at a lower scale, and parts go into the nonperturbative shape function. For , the perturbative series in are of a different character above and below . We introduce a “split matching” method that allows the series in these regions to be treated independently.
Article Text
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