Evidence for the decay $D^0\to K^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$

We present a search for the “wrong-sign” decay $D^0\to K^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ using $9\hspace{0.5em}{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ collisions on and just below the ${\rm Y}\mathrm{}\left(4S\right)\mathrm{}$ resonance. This decay can occur either through a doubly Cabibbo-suppressed process or through mixing to a $D^0$ followed by a Cabibbo-favored process. Our result for the time-integrated wrong-sign rate relative to the decay $D^0\to K^{-}{\pi }^{+}{\pi }^{-}{\pi }^{+}$ is $\left({0.0041}_{-0.0011}^{+0.0012\mathrm{}}\right(\mathrm{stat})\pm 0.0004(\mathrm{syst}\left)\right)\times (1.07\mathrm{}\pm 0.10)(\mathrm{phase}$ space), which has a statistical significance of 3.9 standard deviations.