# QCD corrections to inclusive heavy hadron weak decays at $\Lambda_{\rm QCD}^3 /m_Q^3$

## TL;DR

This paper provides an analytical calculation of QCD corrections to the heavy quark expansion in inclusive heavy hadron decays, improving the precision of CKM matrix element determinations.

## Contribution

It presents the first full analytical calculation of the $
ho_D/m_Q^3$ coefficient with mass dependence, enhancing theoretical predictions for $|V_{cb}|$.

## Key findings

- QCD corrections to the coefficient are explicitly calculated.
- Mass dependence of the coefficient is fully incorporated.
- Results improve the accuracy of CKM matrix element $|V_{cb}|$ extraction.

## Abstract

We present an analytical calculation of the $\alpha_s$ corrections for the coefficient of $\rho_D/m_Q^3$ term in the heavy quark expansion for the inclusive semileptonic decays of heavy hadrons, such as $B \to X_c \ell \bar{\nu}$. The full dependence of the coefficient on the final-state quark mass is taken into account. Our result leads to further improvement of the theoretical predictions for the precision determination of CKM matrix element $|V_{cb}|$.