Shape-Function Effects and Split Matching in B-> Xs l+ l-
Abstract
We derive the triply differential spectrum for the inclusive rare decay B -> Xs l+ l- in the shape function region, in which Xs is jet-like with . Experimental cuts make this a relevant region. The perturbative and non-perturbative parts of the matrix elements can be defined with the Soft-Collinear Effective Theory, which is used to incorporate alphas corrections consistently. We show that, with a suitable power counting for the dilepton invariant mass, the same universal jet and shape functions appear as in B-> Xs gamma and B-> Xu l nu decays. Parts of the usual alphas(m_b) corrections go into the jet function at a lower scale, and parts go into the non-perturbative shape function. For B -> Xs l+ l-, the perturbative series in alphas are of a different character above and below mu=mb. We introduce a ``split matching'' method that allows the series in these regions to be treated independently.
Cite
@article{arxiv.hep-ph/0511334,
title = {Shape-Function Effects and Split Matching in B-> Xs l+ l-},
author = {Keith S. M. Lee and Iain W. Stewart},
journal= {arXiv preprint arXiv:hep-ph/0511334},
year = {2008}
}
Comments
33 pages; journal version