QCD corrections to inclusive heavy hadron weak decays at ${\Lambda }_{\mathrm{QCD}}^3/m_Q^3$

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 $|V_{cb}|$.

Comments: 4 figures