Observation of $D^0\mathrm{\text{−}}{\overline{D}}^0$ Mixing Using the CDF II Detector

We measure the time dependence of the ratio of decay rates for $D^0\to K^{+}{\pi }^{-}$ to the Cabibbo-favored decay $D^0\to K^{-}{\pi }^{+}$. The charge conjugate decays are included. A signal of $3.3\times {10}^4$ $D^{*+}\to {\pi }^{+}{D}^0$, $D^0\to K^{+}{\pi }^{-}$ decays is obtained with $D^0$ proper decay times between 0.75 and 10 mean $D^0$ lifetimes. The data were recorded with the CDF II detector at the Fermilab Tevatron and correspond to an integrated luminosity of $9.6{\mathrm{fb}}^{-1}$ for $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$. Assuming $CP$ conservation, we search for $D^0$-${\overline{D}}^0$ mixing and measure the mixing parameters to be $R_D=(3.51\pm 0.35)\times {10}^{-3}$, $y^{\prime }=(4.3\pm 4.3)\times {10}^{-3}$, and $x^{\prime 2}=(0.08\pm 0.18)\times {10}^{-3}$. We report Bayesian probability intervals in the $x^{\prime 2}$-$y^{\prime }$ plane and find that the significance of excluding the no-mixing hypothesis is equivalent to 6.1 Gaussian standard deviations, providing the second observation of $D^0$-${\overline{D}}^0$ mixing from a single experiment.

Figure 1

Time-integrated distribution for wrong-sign $D^0\to K^{+}{\pi }^{-}$ signal yield as a function of $\Delta M$. The signal yield for each bin of $\Delta M$ is determined from a fit to the corresponding $M_{K\pi }$ distribution. The result of a ${\chi }^2$ fit to the $\Delta M$ distribution is shown.

Figure 2

Measured ratio $R_m$ of wrong-sign to right-sign $D^{*}$ decays as a function of normalized proper decay time. The results of a least-squares fit are shown for $R_m^{\mathrm{pred}}$ (mixing fit) and the prompt component $R$. A fit assuming no mixing is clearly incompatible with the data.

Figure 3

Distribution of transverse impact parameter $d_0$ for right-sign $D^0$ candidates from all $t/\tau$ bins. The narrow peak is due to promptly produced $D^0$ mesons and the broad distribution is due to nonprompt $D^0$ mesons from beauty-particle decay. For candidates with $d_0<60\mu \mathrm{m}$, 95% are produced promptly at the collision point and 5% are nonprompt.

Figure 4

Contours in $x^{\prime 2}\mathrm{\text{−}}{y}^{\prime }$ parameter space bounding regions with Bayesian posterior probability corresponding to 1, 3, and 5 Gaussian standard deviations.