Marching towards a Theory of Non-leptonic Decays of heavy-Flavour Hadrons"

Theoretical descriptions for the nonleptonic decays of heavy flavour hadrons have emerged that incorporate non-perturbative corrections in a systematic way and are genuinely based on QCD. One can reproduce $\tau (D^{+})\mathrm{/}\tau (D^0)$, $B{R}_{SL}(D^{+})$ and $B{R}_{SL}(D^0)$ as due mainly to destructive interference in $D^{+}$ decays; one predicts $\tau (B^{-})$ to exceed $\tau (B_d)$ by a few per cent; $B{R}_{SL}(B)$ is reduced only slightly, raising the prospects of a serious and tantalizing conflict with ARGUS & CLEO data. It is emphasized that the lifetimes for the two mass eigenstates in the $B_s$-${\bar{B}}_s$ system could differ by 30% or even more. The status of phenomenological treatments of non-leptonic two-body modes is briefly reviewed.