Search for flavor-changing-neutral-current and lepton-flavor-violating decays of the $D^0$ meson at BABAR

We search for flavor-changing-neutral-current and lepton-flavor-violating decays of the form $D^0 \to \ell^+ \ell'^- V^0$, where $\ell^+ \ell^{\prime-}$ may be $\mu^+ \mu^-$, $e^+ e^-$, or $\mu^\pm e^\mp$ and $V^0$ is a neutral vector meson. Measurements are based on $425 {\rm fb}^{-1}$ of electron-positron collision events collected with the BABAR detector at the SLAC National Accelerator Laboratory.