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

TL;DR

This paper calculates complete second-order QCD corrections to the leptonic invariant mass spectrum in semileptonic B decays, including triple-charm contributions, to improve the precision of |V_{cb}| extraction.

Contribution

It provides the first full computation of $ ext{O}(oldsymbol{ ext{α}_s^2})$ corrections, including the triple-charm channel, for the leptonic invariant mass spectrum in $b o X_c l ar{ u}_l$ decays.

Findings

Confirmed previous results for single-charm corrections.

Analyzed the impact of triple-charm channel on spectrum moments.

Provided numerical fits for both single- and triple-charm cases.

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.