Search for flavor-changing neutral currents and lepton-family-number violation in two-body $D^0$ decays

We present the results of a search for the three neutral charm decays $D^0\to {\mu }^{\pm }{e}^{\mp },$ $D^0\to {\mu }^{+}{\mu }^{-},$ and $D^0\to e^{+}{e}^{-}.$ This study was based on data collected in Experiment 789 at the Fermi National Accelerator Laboratory using $800\mathrm{GeV}/c$ proton-Au and proton-Be interactions. No evidence is found for any of the decays. Upper limits on the branching ratios, at the 90% confidence level, of $1.56\times {10}^{-5}$ for $D^0\to {\mu }^{+}{\mu }^{-},$ $8.19\times {10}^{-6}$ for $D^0\to e^{+}{e}^{-}$ and $1.72\times {10}^{-5}$ for $D^0\to {\mu }^{\pm }{e}^{\mp }$ are obtained.