  The hadronic matrix elements of dimension-six $\Delta F=0,2$ operators are
crucial inputs for the theory predictions of mixing observables and lifetime
ratios in the $B$ and $D$ system. We determine them using HQET sum rules for
three-point correlators. The results of the required three-loop computation of
the correlators and the one-loop computation of the QCD-HQET matching are given
in analytic form. For mixing matrix elements we find very good agreement with
recent lattice results and comparable theoretical uncertainties. For lifetime
matrix elements we present the first ever determination in the $D$ meson sector
and the first determination of $\Delta B=0$ matrix elements with uncertainties
under control - superseeding preliminary lattice studies stemming from 2001 and
earlier. With our state-of-the-art determination of the bag parameters we
predict: $\tau(B^+)/\tau(B_d^0) = 1.082_{-0.026}^{+0.022}$,
$\tau(B_s^0)/\tau(B_d^0) = 1.0007\pm0.0025$, $\tau(D^+)/\tau(D^0) =
2.7_{-0.8}^{+0.7}$ and the mixing-observables in the $B_s$ and $B_d$ system, in
good agreement with the most recent experimental averages.
