Phenomenology of the $1/m_Q$ Expansion in Inclusive $B$ and $D$ Meson Decays

Abstract

We apply a recent theoretical analysis of hadronic observables in inclusive semileptonic heavy hadron decays to the phenomenology of $B$ and $D$ mesons. Correlated bounds on the nonperturbative parameters $\bar\Lambda$ and $\lambda_1$ are derived by considering data from $B$ decays and, independently, data from $D$ decays. The two sets of bounds are found to be consistent with each other. The data from $B$ decays are then are used to extract a lower limit on the CKM matrix element $|V_{cb}|$. We address the issue of the convergence of the perturbative expansions used in the analysis, and compare our bounds on $\bar\Lambda$ and $\lambda_1$ to lattice and QCD sum rule results. Finally, we argue that a comparison of the analyses of $D$ and $D_s$ decays provides evidence for the applicability of parton-hadron duality in the semileptonic decay of charmed hadrons.