Search for $D^0$ mixing in $D^0\rightarrow K^-\pi^+\pi^-\pi^+$

We report on studies of the right sign and wrong sign decays of $D^0\rightarrow K^- \pi^+ \pi^- \pi^+$ using $230.4~{\rm fb}^{- 1}$ of data collected by the BaBar experiment. The preliminary measurement of the doubly Cabbibo-suppressed rate for the $D^0\rightarrow K^- \pi^+\pi^-\pi^+$ decay is presented, which can provide insights into searching for $D^0$ mixing via this hadronic decay of neutral $D$ meson.