Measurements of Lifetimes and a Limit on the Lifetime Difference in the Neutral<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">D</mml:mi></mml:math>-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 $\ensuremath{\Delta}\ensuremath{\Gamma}$ for the mass eigenstates of the ${D}^{0}$- ${\overline{D}}^{0}$ system. We obtain our result from lifetime measurements of the decays ${D}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ and ${D}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{K}^{+}$, under the assumption of CP invariance, which implies that the CP eigenstates and the mass eigenstates are the same. The lifetime of ${D}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{K}^{+}$ (the CP-even final state) is ${\ensuremath{\tau}}_{\mathrm{KK}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.410\ifmmode\pm\else\textpm\fi{}0.011\ifmmode\pm\else\textpm\fi{}0.006\mathrm{ps}$, and the lifetime of ${D}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ (an equal mixture of CP-odd and CP-even final states) is ${\ensuremath{\tau}}_{K\ensuremath{\pi}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.413\ifmmode\pm\else\textpm\fi{}0.003\ifmmode\pm\else\textpm\fi{}0.004\mathrm{ps}$. The decay-width difference is $\ensuremath{\Delta}\ensuremath{\Gamma}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2({\ensuremath{\Gamma}}_{\mathrm{KK}}\ensuremath{-}{\ensuremath{\Gamma}}_{K\ensuremath{\pi}})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.04\ifmmode\pm\else\textpm\fi{}0.14\ifmmode\pm\else\textpm\fi{}0.05{\mathrm{ps}}^{\ensuremath{-}1}$. We relate these measurements to measurements of mixing in the neutral $D$-meson system.