NNLO corrections to inclusive semileptonic B decays in the shape-function region

TL;DR

This paper calculates the last missing NNLO QCD corrections to inclusive semileptonic B decays in the shape-function region, aiming to improve the precision of |V_ub| extraction.

Contribution

It provides the complete two-loop hard coefficient functions for B -> X_u l nu decays, enabling a full NNLO analysis in this decay region.

Findings

2-loop corrections are free of infrared singularities

Numerical analysis shows NNLO corrections impact decay rate predictions

Charm mass effects are discussed in the context of corrections

Abstract

We compute 2-loop QCD corrections to the hard coefficient functions which arise in the factorization formula for B -> X_u l nu decays in the shape-function region. Our calculation provides the last missing piece required for a NNLO analysis of inclusive semileptonic B decays, which may significantly reduce the theoretical uncertainty in the extraction of the CKM matrix element |V_ub|. Among the technical aspects, we find that the 2-loop hard coefficient functions are free of infrared singularities as predicted by the factorization framework. We perform a brief numerical analysis of the NNLO corrections and include a discussion on charm mass effects.