Heavy Quark Expansions for Inclusive Heavy-Flavour Decays and the Lifetimes of Charm and Beauty Hadrons

Abstract

Inclusive heavy-flavour decays can be described through $1/m_Q$ expansions derived from QCD with the help of an operator product expansion. I sketch their methodology and apply them first to semileptonic B decays; $|V(cb)|$ can be extracted from $\Gamma _{SL}(B)$ and $\bar B \to l \nu D^*$ with the result: $|V(cb)|_{incl} = 0.0413 \pm 0.0016_{exp} \pm 0.002_{theor}$, $|V(cb)|_{excl} = 0.0377 \pm 0.0016_{exp} \pm 0.002_{theor}$. The lifetimes of charm and beauty hadrons are discussed. The charm lifetimes are predicted/reproduced as well as could be expected. Predictions on B meson lifetimes agree with available data; $\Lambda _b$ baryons are predicted to be shorter lived than B_d mesons by no more than ~ 10% - in marked contrast to present measurements. I evaluate the situation and comment on recent theoretical criticism. The importance of the concepts of global vs. local quark-hadron duality is pointed out.