Quark-Hadron Duality Violations and Higher-Order $1/m_b$ Corrections in Inclusive Semileptonic $B$ Decays

Abstract

The theoretical description and data for inclusive semileptonic $B$ decays have reached incredible precision. This motivated us to re-animate the discussion of possible Quark-Hadron Duality violations. There seems that there is currently no evidence of a failure of the Heavy Quark Expansion (HQE) used to compute observables for these decays. However, we might arrive at a point where an asymptotic behaviour of the HQE would limit a further increase of precision. We discuss this possibility and suggest a simple model, which can be used to study the effects of higher orders in the $1/m_b$ expansion and possible quark-hadron duality violations. We devise observables sensitive only to such higher-order effects to test the behaviour of the HQE. Using these observables we obtain a first estimate of possible quark-hadron duality violations using the measured $q^2$ moments.

22 pages, 5 figures

References in corpus (6)

• Three loop calculations and inclusive $V_{cb}$
• Higher Order Power Corrections in Inclusive B Decays
• Third order corrections to the semi-leptonic \boldmath{$b\to c$} and the muon decays
• Improved Estimates for the Parameters of the Heavy Quark Expansion
• NLO QCD Corrections to Inclusive $b\to c\ell \bar{\nu }$ Decay Spectra up to $1/m_Q^3$
• Inclusive Semileptonic $b\to c\ell \bar{\nu }$ Decays to Order $1/m_b^5$