B -> X_u l nu decay distributions to order alpha_s

TL;DR

This work provides analytic O(α_s) corrections to the fully differential B → X_u l ν decay rate in the leading heavy-quark expansion, enabling the computation of arbitrary inclusive distributions with experimental cuts. By deriving the hadronic tensor in terms of five invariant functions and presenting compact double-differential and single-differential results, it establishes a versatile framework for phenomenology, including the hadronic invariant-mass distribution and the lepton-energy spectrum. The paper also incorporates nonperturbative Fermi-motion effects via a shape function, demonstrating substantial impact on spectra and practical utility for |V_ub| extractions, while analyzing the time-like perturbative structure to assess duality reliability. Together, these results provide a comprehensive, analytic toolkit for precision inclusive B decays with controlled perturbative and nonperturbative effects.

Abstract

An analytic result for the O(alpha_s corrections to the triple differential B -> X_u l nu decay rate is presented, to leading order in the heavy-quark expansion. This is relevant for computing partially integrated decay distributions with arbitrary cuts on kinematic variables. Several double and single differential distributions are derived, most of which generalize known results. In particular, an analytic result for the O(alpha_s) corrections to the hadronic invariant mass spectrum is presented. The effects of Fermi motion, which are important for the description of decay spectra close to infrared sensitive regions, are included. The behaviour of perturbation theory in the region of time-like momenta is also investigated