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arXiv · 2601.15447

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

A. Broggio·B. Capdevila·A. Ferroglia·P. Gambino
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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.

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A. Broggio, B. Capdevila, A. Ferroglia, P. Gambino. 2026-01-21. Structure functions for the inclusive semileptonic $b$-quark decay at NNLO: a semi-analytic calculation. https://arxiv.org/abs/2601.15447

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