Measurements of Lifetimes and a Limit on the Lifetime Difference in the NeutralD-Meson System

Using the large hadroproduced charm sample collected in experiment E791 at Fermilab, we report the first directly measured constraint on the decay-width difference $\Delta \Gamma$ for the mass eigenstates of the $D^0$- ${\overline{D}}^0$ system. We obtain our result from lifetime measurements of the decays $D^0\to K^{-}{\pi }^{+}$ and $D^0\to K^{-}{K}^{+}$, under the assumption of CP invariance, which implies that the CP eigenstates and the mass eigenstates are the same. The lifetime of $D^0\to K^{-}{K}^{+}$ (the CP-even final state) is ${\tau }_{\mathrm{KK}}=0.410\mathrm{}\pm 0.011\pm 0.006\mathrm{ps}$, and the lifetime of $D^0\to K^{-}{\pi }^{+}$ (an equal mixture of CP-odd and CP-even final states) is ${\tau }_{K\pi }=0.413\mathrm{}\pm 0.003\pm 0.004\mathrm{ps}$. The decay-width difference is $\Delta \Gamma =2\mathrm{}({\Gamma }_{\mathrm{KK}}-{\Gamma }_{K\pi })=0.04\mathrm{}\pm 0.14\pm 0.05{\mathrm{ps}}^{-1\mathrm{}}$. We relate these measurements to measurements of mixing in the neutral $D$-meson system.