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

We measure the time dependence of the ratio of decay rates for the rare decay $D^0 \rightarrow K^+\pi^-$ to the Cabibbo-favored decay $D^0 \rightarrow K^-\pi^+$. We use a signal of $12.7 \times 10^3$ $D^0 \rightarrow K^+\pi^-$ decays with proper decay times between 0.75 and 10 mean $D^0$ lifetimes. The data sample was recorded with the CDF~II detector at the Fermilab Tevatron and corresponds to an integrated luminosity of 1.5 fb$^{-1}$ for $p\bar{p}$ collisions at $\sqrt{s}$ = 1.96 TeV. We search for $D^0$-$\bar{D}^0$ mixing and measure the mixing parameters to be $R_D = (3.04 \pm 0.55) \times 10^{-3}$, $y' = (8.5 \pm 7.6) \times 10^{-3}$, and $x'^2 = (-0.12 \pm 0.35) \times 10^{-3}$. We report Bayesian probability contours in the $x'^2$-$y'$ plane and find that the data are inconsistent with the no-mixing hypothesis with a probability equivalent to 3.8 Gaussian standard deviations. Potential updates to the analysis will be presented.