One-loop QCD corrections to $$ \overline{B}\to {X}_c\ell {\overline{\nu}}_{\ell } $$ in and beyond the Standard Model

A bstract We compute one-loop QCD corrections to the triple differential width of the inclusive decay $$ \overline{B}\to {X}_c\ell {\overline{\nu}}_{\ell } $$ B ¯ → X c ℓ ν ¯ ℓ including contributions from all relevant dimension-six operators in the Weak Effective Theory (WET), at leading power in the heavy quark expansion. Furthermore we derive for the first time up to order $$ \mathcal{O}\left({\alpha}_s\right) $$ O α s analytic expressions for the first three moments of the distribution in the lepton energy, hadronic invariant mass and dilepton invariant mass, in the presence of beyond the Standard Model contributions from the WET.