$D_s$ Lifetime, $m_b$, $m_c$ and $|V_{cb}|$ in the Heavy Quark Expansion

Abstract

We present some straightforward applications of the QCD heavy quark expansion, stated in previous papers [1-3], to the inclusive widths of heavy flavour hadrons. We address the question of the $D_s$ lifetime and argue that -- barring Weak Annihilation (WA) -- $\tau (D_s)$ is expected to exceed $\tau (D^0)$ by several percent; on the other hand WA could provide a difference of up to $10÷20\%$ of {\it any} sign. We extract $m_c$, $m_b$ and $|V_{cb}|$ from $\Gamma \text{ind}SL(D^{+})$ and $\Gamma \text{ind}SL(B)$. The values of the quark masses are somewhat higher, but compatible with estimates from QCD sum rules; we obtain $|V_{cb}|\simeq 0.043$ for $\tau (B)=1.4$ psec and $B{R}_{SL}(B)=10.5$\% . We discuss the associated uncertainties in the $1/m_Q$ expansion as well as some consequences for other electroweak decays.

Comments: 18 pages Preprint UND-HEP-93-BIG05, CERN-TH.7063/93; this is the revised version. Summary of changes: The discussion of uncertainties in the $1/m_Q$ expansion was shortend as the more detailed one was presented in our recent paper ref.[16] and is due in the forthcoming paper [17]. The sections 3 and 4 are then combined