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 $m{X}^2\lesssim mb{\Lambda }_{Q}CD$. 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.

33 pages; journal version

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• Designing Gapped Soft Functions for Jet Production
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• Logarithmically Enhanced Corrections to the Decay Rate and Forward Backward Asymmetry in anti-B --> X(s) l+ l-
• Radiative and Electroweak Penguin Decays of B Mesons
• Extracting short distance information from b -> s l+ l- effectively
• Precise predictions for B -> Xs l+ l- in the large q^2 region
• Heavy-to-light currents at NNLO in SCET and semi-inclusive anti-B ---> X(s) l+ l- decay
• Precision Global Determination of the $B\to X_s\gamma$ Decay Rate
• Long distance effects in inclusive rare $B$ decays and phenomenology of $\bar{B}\to X_d{\ell }^{+}{\ell }^{-}$
• Nonperturbative m_X cut effects in B -> Xs l+ l- observables
• Status of SM calculations of b > s transitions
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• Subleading Shape-Function Effects and the Extraction of |V_ub|