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  • Access by Xinjiang University

Shape-function effects and split matching in BXs+

Keith S. M. Lee* and Iain W. Stewart

  • 1Center for Theoretical Physics, Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

  • *Electronic address: ksml@mit.edu
  • Electronic address: iains@mit.edu

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 BXs+ in the shape-function region, in which Xs is jetlike with mX2mbΛQCD. 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 αs 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 BXsγ and BXuν¯ decays. Parts of the usual αs(mb) corrections go into the jet function at a lower scale, and parts go into the nonperturbative shape function. For BXs+, the perturbative series in αs are of a different character above and below μ=mb. We introduce a “split matching” method that allows the series in these regions to be treated independently.

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