Evidence for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>D</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:mtext mathvariant="normal">−</mml:mtext><mml:msup><mml:mover accent="true"><mml:mi>D</mml:mi><mml:mo stretchy="true">¯</mml:mo></mml:mover><mml:mn>0</mml:mn></mml:msup></mml:math>Mixing

We present evidence for ${D}^{0}\mathrm{\text{\ensuremath{-}}}{\overline{D}}^{0}$ mixing in ${D}^{0}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ decays from $384\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of ${e}^{+}{e}^{\ensuremath{-}}$ colliding-beam data recorded near $\sqrt{s}=10.6\text{ }\text{ }\mathrm{GeV}$ with the BABAR detector at the PEP-II storage rings at the Stanford Linear Accelerator Center. We find the mixing parameters ${x}^{\ensuremath{'}2}=[\ensuremath{-}0.22\ifmmode\pm\else\textpm\fi{}0.30(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.21(\mathrm{syst})]\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ and ${y}^{\ensuremath{'}}=[9.7\ifmmode\pm\else\textpm\fi{}4.4(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}3.1(\mathrm{syst})]\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ and a correlation between them of $\ensuremath{-}0.95$. This result is inconsistent with the no-mixing hypothesis with a significance of 3.9 standard deviations. We measure ${R}_{D}$, the ratio of doubly Cabibbo-suppressed to Cabibbo-favored decay rates, to be $[0.303\ifmmode\pm\else\textpm\fi{}0.016(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.010(\mathrm{syst})]%$. We find no evidence for $CP$ violation.

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