2005/11/30 by Keith S. M. Lee, Iain W. Stewart
Physics and Astronomy · #Black Holes and Theoretical Physics #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-ph
paper · pdf · doi:10.1103/physrevd.74.014005
published as Phys.Rev.D74:014005,2006 · 33 pages; journal version
arxiv created 2006/06/30 · openalex publication_date 2006/07/07 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We derive the triply differential spectrum for the inclusive rare decay B\ensuremath→Xs\ensuremathℓ+\ensuremathℓ^\ensuremath- in the shape-function region, in which Xs is jetlike with mX2\ensuremath\lesssimmb\ensuremathΛQCD. 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 \ensuremathαs 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 B\ensuremath→Xs\ensuremathγ and B\ensuremath→Xu\ensuremathℓ\ensuremathν decays. Parts of the usual \ensuremathαs(mb) corrections go into the jet function at a lower scale, and parts go into the nonperturbative shape function. For B\ensuremath→Xs\ensuremathℓ+\ensuremathℓ^\ensuremath-, the perturbative series in \ensuremathαs are of a different character above and below \ensuremathμ=mb. We introduce a ``split matching'' method that allows the series in these regions to be treated independently.