Complete \( \mathcal{O}\left({\alpha}_s^2\right) \) corrections to the leptonic invariant mass spectrum in \( b\to {X}_cl{\overline{\nu}}_l \) decay

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 \( \mathcal{O}\left({\alpha}_s^2\right) \) corrections to the analogous spectrum in the partonic \( b\to {X}_cl{\overline{\nu}}_l \) 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 \( cc\overline{c}l{\overline{\nu}}_l \) 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.