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arXiv · 2411.12866

Complete $\mathcal{O}(\alpha_s^2)$ Corrections to the Leptonic Invariant Mass Spectrum in $b\to X_c l\bar{\nu}_l$ Decay

Mateusz Czaja·Mikołaj Misiak·Abdur Rehman
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Abstract

In the determination of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$ from inclusive semileptonic $B$-meson decays, moments of the leptonic invariant mass spectrum constitute valuable observables. To evaluate them with sufficient precision, perturbative $\mathcal{O}(\alpha_s^2)$ corrections to the analogous spectrum in the partonic $b\to X_c l\bar{\nu}_l$ decay are necessary. In the present paper, we compute such perturbative corrections in a complete manner, including contributions from the triple-charm channel, namely from the $cc\bar{c}l\bar{\nu}_l$ final states. We present our results in terms of numerical fits in both the single- and triple-charm cases. We confirm the recently found results for the single-charm correction, and analyze the triple-charm channel impact on centralized moments of the spectrum.

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Mateusz Czaja, Mikołaj Misiak, Abdur Rehman. 2024-11-19. Complete $\mathcal{O}(\alpha_s^2)$ Corrections to the Leptonic Invariant Mass Spectrum in $b\to X_c l\bar{\nu}_l$ Decay. https://arxiv.org/abs/2411.12866

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