Extracting $\mathrm{\mid }{V}_{bc}\mathrm{\mid }$, $m_c$ and $m_b$ from Inclusive $D$ and $B$ Decays

Using recent results for nonperturbative contributions to the $B$ and $D$ meson inclusive semileptonic widths, a model independent extraction of $\text{vbc}$, $m_c$ and $m_b$ is made from the experimentally measured $B$ and $D$ lifetimes and semileptonic branching ratios. Constraining the parameters of the HQET at $\text{CO}(1\mathrm{/}{m}_Q^2)$ by the $D$ semileptonic width, $\text{vbc}$ is found to lie in the range $.040<\text{vbc}<0.057$. The $c$ and $b$ quark masses are not well constrained due to uncertainty in the relevant scale of ${\alpha }_s$. These results assume the validity of perturbative QCD at the low scales relevant to semileptonic charm decay. Without making this assumption, somewhat less stringent bounds on $V_{bc}$ from $B$ decay alone may be obtained.