Measurement of $D^0\mathrm{\text{−}}{\overline{D}}^0$ mixing using the ratio of lifetimes for the decays $D^0\to K^{-}{\pi }^{+}$ and $K^{+}{K}^{-}$

We measure the rate of $D^0\mathrm{\text{−}}{\overline{D}}^0$ mixing with the observable $y_{CP}=({\tau }_{K\pi }/{\tau }_{KK})-1$, where ${\tau }_{KK}$ and ${\tau }_{K\pi }$ are, respectively, the mean lifetimes of $CP$-even $D^0\to K^{+}{K}^{-}$ and $CP$-mixed $D^0\to K^{-}{\pi }^{+}$ decays, using a data sample of $384{\mathrm{fb}}^{-1}$ collected by the BABAR detector at the SLAC PEP-II asymmetric-energy $B$ Factory. From a sample of $D^0$ and ${\overline{D}}^0$ decays where the initial flavor of the decaying meson is not determined, we obtain $y_{CP}=[1.12\pm 0.26(\mathrm{stat})\pm 0.22(\mathrm{syst})]\%$, which excludes the no-mixing hypothesis at $3.3\sigma$, including both statistical and systematic uncertainties. This result is in good agreement with a previous BABAR measurement of $y_{CP}$ obtained from a sample of $D^{*+}\to D^0{\pi }^{+}$ events, where the $D^0$ decays to $K^{-}{\pi }^{+}$, $K^{+}{K}^{-}$, and ${\pi }^{+}{\pi }^{-}$, which is disjoint with the untagged $D^0$ events used here. Combining the two results taking into account statistical and systematic uncertainties, where the systematic uncertainties are assumed to be 100% correlated, we find $y_{CP}=[1.16\pm 0.22(\mathrm{stat})\pm 0.18(\mathrm{syst})]\%$, which excludes the no-mixing hypothesis at $4.1\sigma$.

Figure 1

(a) $D^0\to K^{-}{\pi }^{+}$ and (b) $D^0\to K^{+}{K}^{-}$ invariant mass distribution with the data (points), total fit (line) and background contribution (solid) overlaid. The innermost dashed lines on either side of the signal peaks delimit the lifetime fit mass region, with lower and upper mass sidebands shown on either side.

Figure 2

$D^0\to K^{-}{\pi }^{+}$ decay time distribution with the data (points), total lifetime fit (line), signal (white), combinatorial background (gray) and charm background (black) contributions overlaid.

Figure 3

$D^0\to K^{+}{K}^{-}$ decay time distribution with the data (points), total lifetime fit (line), signal (white), combinatorial background (gray) and charm background (black) contributions overlaid.