Evidence for $D^0-{\overline{D}}^0$ Mixing Using the CDF II Detector

We measure the time dependence of the ratio of decay rates for the rare decay $D^0\to K^{+}{\pi }^{-}$ to the Cabibbo-favored decay $D^0\to K^{-}{\pi }^{+}$. A signal of $12.7\times {10}^3$ $D^0\to K^{+}{\pi }^{-}$ decays was obtained using the Collider Detector at Fermilab II detector at the Fermilab Tevatron with an integrated luminosity of $1.5{\mathrm{fb}}^{-1}$. We measure the $D^0-{\overline{D}}^0$ mixing parameters $(R_D,y^{\prime },x^{\prime 2})$, and find that the data are inconsistent with the no-mixing hypothesis with a probability equivalent to 3.8 Gaussian standard deviations.

Figure 1

(left) Time-integrated distribution for “wrong-sign” $D^0\to K^{+}{\pi }^{-}$ signal yield as a function of $\Delta m$. Also shown is the result of a least-squares fit using an empirical function for the signal (dark shaded region) and a power law for the background (light shaded region). (right) Distribution of transverse impact parameter $d_0$ for $D^0$ mesons with $5<t/\tau <6$ for “right-sign” $D^{*}$ mesons. The result of a binned maximum likelihood fit shows the narrow peak due to promptly produced $D^{*}$ mesons (dark shaded) and the broad distribution due to nonprompt $D^{*}$ mesons from $B$ decay (light shaded).

Figure 2

(left) Ratio of prompt $D^{*}$ “wrong-sign” to “right-sign” decays as a function of normalized proper decay time. The dashed curve is from a least-squares parabolic fit, which determines the parameters $R_D$, $y^{\prime }$, and $x^{\prime 2}$. The dotted line is the fit assuming no mixing. (right) Bayesian probability contours in the $x^{\prime 2}-y^{\prime }$ parameter space corresponding to one through four equivalent Gaussian standard deviations. The closed circle shows the unconstrained fit values for the mixing parameters. The open diamond shows the values from the physically allowed fit ($x^{\prime 2}\ge 0$). The cross shows the no-mixing point.