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

TL;DR

This paper examines the potential limitations of the Heavy Quark Expansion in inclusive semileptonic B decays, proposing models and observables to detect higher-order effects and possible duality violations.

Contribution

It introduces a simple model to study higher-order $1/m_b$ corrections and duality violations, and proposes observables to test the HQE's asymptotic behavior.

Findings

No current evidence of duality violations in data.

Proposed observables are sensitive to higher-order effects.

First estimate of duality violations using $q^2$ moments.

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.