Charm Decays and Spectroscopy at BABAR

We present searches for rare charm decays of the form $X_c^+ \to h^{\pm} \ell^{\mp} \ell^{(‘)^+}$,where$X_c^+$isacharmhadroneither$D^+$,$D_s^+$,or$\Lambda_c^+$,and$\ell^{(’)^{\pm}}$ is an electron or muon. These modes are based on 384 $f{b}^{-1}$ of $e^{+}{e}^{-}$ annihilation data collected at the $\mathrm{{\rm Y}}(4S)$ resonance with the BABAR detector at the SLAC National Accelerator Laboratory. We also present the flavor-changing neutral-current decays $D^0\to e^{+}{e}^{-}$, $D^0\to {\mu }^{+}{\mu }^{-}$, and $D^0\to e^{\pm }{\mu }^{\mp }$ that corresponds to an integrated luminosity of 468 $f{b}^{-1}$ of data. The decay $D^0\to e^{+}{\mu }^{-}$ is further lepton-flavor violating, and thus occur only through very slow neutrino mixing. These decays constitute sensitive probes for possible new-physics contribution. We report new limits on the branching fractions of these decays.