New physics contributions to moments of inclusive $b \to c$ semileptonic decays

Inclusive semileptonic $B\to X_c \ell \bar{\nu}_\ell$ decays, where $\ell = \mu,e$, are by now standard candles in the determination of the CKM element $|V_{cb}|$. These determinations rely on the heavy-quark expansion and use moments of decay spectra to extract the non-perturbative parameters directly from data under the standard model assumption. At the same time, new physics could influence the moments of the inclusive decay. In this paper, we compute power-corrections and next-to-leading order corrections in the strong coupling constant using the full basis of dimension-six new physics operators for the inclusive $B \to X_c \ell \bar{\nu}$ decay. We provide predictions for lepton energy, hadronic and leptonic invariant mass moments, and perform a phenomenological study to show the possible impact of new physics. Our results could be used to perform a global fit including new physics contributions.