Exact dependence of inclusive rates on the b-quark mass beyond HQE

Determine the exact dependence on the b-quark mass m_b of the total inclusive semileptonic B→X_cℓν decay rate beyond the heavy-quark expansion approximation, in order to assess and model possible duality-violating contributions.

Background

Because the heavy-quark expansion is the only practical tool for inclusive semileptonic decays, the exact functional dependence of observables on m_b is unknown. This limits direct, first-principles assessments of duality violations and necessitates modeling approaches.

Clarifying the exact m_b-dependence would provide a benchmark to test the asymptotic behavior assumptions and the magnitude of duality-violating terms proposed in the paper.