Complete O α s 2 $$ \mathcal{O}\left(α_s^2\right) $$ corrections to the leptonic invariant mass spectrum in b → X c l ν ¯ l $$ b→ X_cl{\overline{ν}}_l $$ decay - Mateusz Czaja; Mikołaj Misiak; Abdur Rehman (Journal of High Energy Physics)
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 O α s 2 $$ \mathcal{O}\left(α_s^2\right) $$ corrections to the analogous spectrum in the partonic b → X c l ν ¯ l $$ b→ X_cl{\overline{ν}}_l $$ 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 c ¯ l ν ¯ l $$ cc\overline{c}l{\overline{ν}}_l $$ 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.