Extracting |V_{ub}| from the Hadronic Mass Spectrum of Inclusive B decays

TL;DR

This work targets a precise determination of |V_{ub}| from inclusive B decays by employing a hadronic invariant mass cut to mitigate Fermi-motion uncertainties. It develops an infrared-factorization framework with resummation for the cut hadronic mass spectrum and leverages a universal soft function linked to a nonperturbative structure function, using Mellin moments to relate hadronic and radiative decay spectra. A closed-form expression for the ratio |V_{ub}|/|V_{ts}| is obtained in terms of the cut-rate δΓ(c) and radiative decay data, enabling a determination with an estimated theoretical uncertainty around 5% (modulo duality violations). The approach relies on B→X_sγ data to cancel nonperturbative pieces and emphasizes experimental resolution as a key factor for viability and cross-checks with alternative extractions.

Abstract

Following a strategy introduced earlier by the authors, we show that it is possible to extract |V_{ub}| from the cut hadronic mass spectrum of B decays without large systematic errors which usually arise from having to model the Fermi motion of the heavy quark. We present a closed form expression for |V_{ub}|/|V_{ts}| which is accurate up to corrections of order α_s^2, α_s ρ, (Λ/m_b)^2/ρ, where ρis the experimental cut (s_c/m_b^2) on the hadronic mass used to veto charmed decays. Modulo duality violation errors, which are intrinsic to all inclusive predictions, we estimate the theoretical error in the extraction to be at the 5% level.

Figures (1)

• Figure 1: Percentage change due to resummation. The solid line is the fully resummed result. The dotted line is the expansion of the resummed result to order $\alpha_s$, while the dot-dashed line is the expansion of the resummed result up to order $\alpha_s^2$.