Rate Measurement of ${\mathit{D}}^0\to {\mathit{K}}^{+}{\pi }^{-}{\pi }^0$ and Constraints on ${\mathit{D}}^0-\overline{{\mathit{D}}^0}$ Mixing

We present an observation and time-integrated rate measurement of the decay $D^0\to K^{+}{\pi }^{-}{\pi }^0$ produced in $9{\mathrm{fb}}^{-1\mathrm{}}$ of $e^{+}{e}^{-}$ collisions near the $\Upsilon \left(4S\right)$ resonance. The signal is inconsistent with an upward fluctuation of the background by 4.9 standard deviations. We measured the time-integrated rate of $D^0\to K^{+}{\pi }^{-}{\pi }^0$ normalized to the rate of $\overline{D^0}\to K^{+}{\pi }^{-}{\pi }^0$ to be ${0.0043}_{-0.0010\mathrm{}}^{+0.0011\mathrm{}}\left(\mathrm{stat}\right)\pm 0.0007\left(\mathrm{syst}\right)$. This decay can be produced by doubly Cabibbo-suppressed decays or by the $D^0$ evolving into a $\overline{D^0}$ through mixing, followed by a Cabibbo-favored decay to $K^{+}{\pi }^{-}{\pi }^0$. We also found the $\mathrm{CP}$ asymmetry $A=\left(9_{-22\mathrm{}}^{+25\mathrm{}}\right)\%$ be consistent with zero.