Limits on $D^0$-$\bar D^0$ mixing and $CP$ violation from the ratio of lifetimes for decay to $K^-\pi^+$, $K^-K^+$, and $\pi^-\pi

We present a measurement of $D^0$-$\D0bar$ mixing parameters using the ratios of lifetimes extracted from samples of $D^0$ mesons decaying to $K^-\pi^+$, $K^-K^+$, and $\pi^-\pi^+$. Using 91 ${\rm fb}^{-1}$ of data collected by the BaBar detector at the PEP-II asymmetric-energy $B$ Factory, we obtain a value $Y = (0.8 \pm 0.4 ({\rm stat.}) {}^{+0.5}_{-0.4} ({\rm syst.}))$%, which, in the limit of CP conservation, corresponds to the mixing parameter $y = \Delta\Gamma/2\Gamma$. Using the difference in lifetimes of $D^0$ and $\D0bar$ mesons, we obtain the CP-violation parameter $\Delta Y = (-0.8 \pm 0.6 ({\rm stat.}) \pm 0.2 ({\rm syst.}))$%.