Lifetime differences in heavy mesons with time independent measurements

Heavy meson pairs produced in the decays of heavy quarkonium resonances at $e^{+}{e}^{-}$ machines (beauty and tau-charm factories) have the useful property that the two mesons are in the $CP$-correlated states. We show that this leads to time-independent correlations allowing the extraction of the lifetime difference $\Delta {\Gamma }_D$ and other mixing parameters. In particular, for the decay $\psi (3770)\to D^0{\overline{D}}^0$ the correlation of a flavor specific decay of one $D$ with a $CP$-specific decay of the other $D$ is linearly sensitive to the $D^0$ lifetime difference. The utility of this method is considered at CLEO-c as well as future threshold charm factories. We include the impact of possible $CP$-violating effects and present the complete results for time-integrated $CP$-entangled decay rates with $CP$ violation taken into account. We comment on the utility of using this method to extract the lifetime difference of neutral $B$ mesons at future high luminosity $B$ factories.