Eur. Phys. J. C (2010) 65: 501-515
https://doi.org/10.1140/epjc/s10052-009-1210-0

Regular Article - Theoretical Physics

NNLO corrections to and the determination of |V _ub |

¹ Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, 3012, Bern, Switzerland
² Johannes Gutenberg-Universität, 55099, Mainz, Germany

^* e-mail: pecjak@thep.physik.uni-mainz.de

Received: 14 September 2009
Published online: 26 November 2009

Abstract

We study the impact of next-to-next-to-leading order (NNLO) QCD corrections on partial decay rates in 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 μ _i ∼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-β ₀ approximation. For the default choice μ _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 μ _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.