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

Physics – High Energy Physics – High Energy Physics - Phenomenology

Scientific paper

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18 pages, 3 embedded figures, uses REVTeX and epsf.sty; this is the slightly revised version to appear in Physical Review D

Scientific paper

10.1103/PhysRevD.53.6316

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.

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