Structure functions for the inclusive semileptonic $b$-quark decay at NNLO: a semi-analytic calculation

TL;DR

This paper computes the hadronic structure functions for inclusive semileptonic $b$-quark decay at NNLO in QCD using a semi-analytic, phase-space slicing approach, enabling precise predictions of decay distributions.

Contribution

It provides the first semi-analytic calculation of structure functions at NNLO for $b$-quark decay, combining numerical and theoretical methods for improved accuracy.

Findings

Good agreement with existing results for decay distributions

Enhanced precision in structure function modeling at NNLO

Validated approach for future decay analyses

Abstract

We present a study of the inclusive charmless semileptonic $b$ decay, $b\to X_u\ell\bar{\nu}$ at next-to-next-to-leading order (NNLO) in perturbative QCD, with the primary aim of extracting the hadronic structure functions $W_i$ at NNLO. The analysis is based on a numerical calculation of the relevant kinematic distributions using a phase-space slicing method to handle infrared-sensitive contributions from real gluon emissions. We use known results from Heavy Quark Effective Theory and Soft-Collinear Effective Theory to extract the singular terms and construct a model for the regular contributions to the structure functions at NNLO, then perform a fit to the numerical results. We use our approximate structure functions to compute various kinematic distributions and moments: the comparison with existing analytic and numerical results shows very good agreement, which is further improved including the available analytic results in the fit.