NNLO corrections to B --> X_u l nu in the shape-function region

TL;DR

This paper calculates the NNLO perturbative corrections to the hard-scattering kernel in the B to X_u l nu decay within the shape-function region, improving theoretical precision for CKM matrix element extraction.

Contribution

It provides the first NNLO calculation of the hard function H, completing the perturbative component of the decay's factorization formula.

Findings

NNLO corrections to the hard function H are computed.

The calculation completes the NNLO perturbative framework for the decay.

Results enhance the precision of theoretical predictions for B decay measurements.

Abstract

The inclusive decay B --> X_u l nu is of much interest because of its potential to constrain the CKM element |V_ub|. Experimental cuts required to suppress charm background restrict measurements of this decay to the shape-function region, where the hadronic final state carries a large energy but only a moderate invariant mass. In this kinematic region, the differential decay distributions satisfy a factorization formula of the form $H \cdot J \otimes S$, where S is the non-perturbative shape function, and the object $H \cdot J$ is a perturbatively calculable hard-scattering kernel. In this paper we present the calculation of the hard function H at next-to-next-to-leading order (NNLO) in perturbation theory. Combined with the known NNLO result for the jet function J, this completes the perturbative part of the NNLO calculation for this process.