Search for lepton-flavor violating decays $D^0\to X^0{e}^{\pm }{\mu }^{\mp }$

We present a search for seven lepton-flavor-violating neutral charm decays of the type $D^0\to X^0{e}^{\pm }{\mu }^{\mp }$, where $X^0$ represents a ${\pi }^0$, $K_{\mathrm{S}}^0$, $\overline{K^{\ast 0}}$, ${\rho }^0$, $\varphi$, $\omega$, or $\eta$ meson. The analysis is based on $468$ fb${}^{-1}$ of $e^{+}{e}^{-}$ annihilation data collected at or close to the $\mathrm{{\rm Y}}(4S)$ resonance with the BaBar detector at the SLAC National Accelerator Laboratory. No significant signals are observed, and we establish 90% confidence level upper limits on the branching fractions in the range $(5.0-22.5)\times {10}^{-7}$. The limits are between one and two orders of magnitude more stringent than previous measurements.