NNLO corrections to B --> X_u l nu and the determination of |V_ub|

Abstract

We study the impact of next-to-next-to-leading order (NNLO) QCD corrections on partial decay rates in B --> X_u l nu decays, at leading-order in the 1/m_b expansion for shape-function kinematics. These corrections are implemented within a modified form of the BLNP framework, which allows for arbitrary variations of the jet scale mu_i \sim 1.5 GeV. Our analysis includes a detailed comparison between resummed and fixed-order perturbation theory, and between the complete NNLO results and those obtained in the large-${\beta }_0$ approximation. For the default choice mu_i=1.5 GeV used in current extractions of |V_ub| within the BLNP framework, the NNLO corrections induce significant downward shifts in the central values of partial decay rates with cuts on the hadronic variable P_+, the hadronic invariant mass, and the lepton energy. At the same time, perturbative uncertainties are reduced, especially those at the jet scale, which are the dominant ones at next-to-leading order (NLO). For higher values of mu_i and in fixed-order perturbation theory, the shifts between NLO and NNLO are more moderate. We combine our new results with known power-suppressed terms in order to illustrate the implications of our analysis on the determination of |V_ub| from inclusive decays.

24 pages, 7 figures

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• On the $O({\alpha }_s^2)$ corrections to $b\to X_{u}e\bar{\nu }$ inclusive decays
• Measurement of the inclusive electron spectrum from B meson decays and determination of |Vub|
• Master Integrals for double real radiation emission in heavy-to-light quark decay
• Potential and limitations of machine-learning approaches to inclusive $|V_{ub}|$ determinations