Measurement of<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>¯</mml:mo></mml:mover><mml:mn>0</mml:mn></mml:msup></mml:math>Mixing from a Time-Dependent Amplitude Analysis of<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:mo>→</mml:mo><mml:msup><mml:mi>K</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup></mml:math>Decays

We present evidence of ${D}^{0}\mathrm{\text{\ensuremath{-}}}{\overline{D}}^{0}$ mixing using a time-dependent amplitude analysis of the decay ${D}^{0}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$ in a data sample of $384\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ collected with the BABAR detector at the PEP-II ${e}^{+}{e}^{\ensuremath{-}}$ collider at the Stanford Linear Accelerator Center. Assuming $CP$ conservation, we measure the mixing parameters ${x}_{K\ensuremath{\pi}{\ensuremath{\pi}}^{0}}^{\ensuremath{'}}=[{2.61}_{\ensuremath{-}0.68}^{+0.57}(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.39(\mathrm{syst})]%$, ${y}_{K\ensuremath{\pi}{\ensuremath{\pi}}^{0}}^{\ensuremath{'}}=[\ensuremath{-}{0.06}_{\ensuremath{-}0.64}^{+0.55}(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.34(\mathrm{syst})]%$. This result is inconsistent with the no-mixing hypothesis with a significance of 3.2 standard deviations. We find no evidence of $CP$ violation in mixing.

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