Dimension-six matrix elements for meson mixing and lifetimes from sum rules

The hadronic matrix elements of dimension-six $\mathrm{\Delta }F=0,2$ 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 $\mathrm{\Delta }B=0$ 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: $\tau (B^{+})\mathrm{/}\tau (B_d^0)=1.082_{-0.026}^{+0.022}$, $\tau (B_s^0)\mathrm{/}\tau (B_d^0)=1.0007\pm 0.0025$, $\tau(D^+)/\tau(D^0) = 2.7_{-0.8}^{+0.7}$andthemixing-observablesinthe$B_s$and$B_d$ system, in good agreement with the most recent experimental averages.