Treating the b quark distribution function with reliable uncertainties

Abstract

The parton distribution function for a b quark in the B meson (called the shape function) plays an important role in the analysis of the B -> X_s gamma and B -> X_u l nu data, and gives one of the dominant uncertainties in the determination of |Vub|. We introduce a new framework to treat the shape function, which consistently incorporates its renormalization group evolution and all constraints on its shape and moments in any short distance mass scheme. At the same time it allows a reliable treatment of the uncertainties. We develop an expansion in a suitable complete set of orthonormal basis functions, which provides a procedure for systematically controlling the uncertainties due to the unknown functional form of the shape function. This is a significant improvement over fits to model functions. Given any model for the shape function, our construction gives an orthonormal basis in which the model occurs as the first term, and corrections to it can be studied. We introduce a new short distance scheme, the "invisible scheme", for the kinetic energy matrix element, lambda_1. We obtain closed form results for the differential rates that incorporate perturbative corrections and a summations of logarithms at any order in perturbation theory, and present results using known next-to-next-to-leading order expressions. The experimental implementation of our framework is straightforward.

26 pages, 14 figures, v2: minor changes, refs added, v3: journal version

References in corpus (10)

• Estimate of BR(B -> X_s gamma) at O(alpha_s^2)
• Top Jets in the Peak Region: Factorization Analysis with NLL Resummation
• Inclusive semileptonic B decays and the determination of |V_ub|
• Designing Gapped Soft Functions for Jet Production
• Analysis of Br(B-->X_s gamma) at NNLO with a Cut on Photon Energy
• Towards $B\to V\gamma$ Decays at NNLO in SCET
• Two-loop Jet-Function and Jet-Mass for Top Quarks
• Enhanced Non-local Power Corrections to the B->X_s+gamma Decay Rate
• Extracting short distance information from b -> s l+ l- effectively
• Subleading Shape-Function Effects and the Extraction of |V_ub|

Cited by in corpus (4)

• Effective Predictions of Event Shapes: Factorized, Resummed, and Gapped Angularity Distributions
• Nonperturbative m_X cut effects in B -> Xs l+ l- observables
• QCD Calculations of Radiative B Decays
• Probing the Structure of Jets: Factorized and Resummed Angularity Distributions in SCET