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at or close to the Υ(4S) resonance with the BaBar detector at the SLAC National Accelerator Laboratory. We find the D0→K−π+e+e− branching fraction in the invariant mass range 0.675 < m(e+e−) < 0.875 GeV/c2 of the electron-positron pair to be B(D0 → K−π+e+e−) = (4.0± 0.5± 0.2± 0.1)× 10−6, where the first uncertainty is statistical, the second systematic, and the third due to the uncertainty in the branching fraction of the decay D0 → K−π+π+π− used as a normalization mode. In a set of regions of m(e+e−) where long-distance effects are potentially small, we determine a 90% confidence level (C.L.) upper limit on the branching fraction B(D0→ K−π+π+π−)< 3.1×10−6. No significant signal is observed for any of the LFV and LNV modes, and we establish 90% C.L. upper limits on the branching fractions in the range (1.0− 30.6)× 10−7. The limits are between one and three orders of magnitude more stringent than previous

Search for lepton-flavour violating and lepton-number violating decays of the $D^0$ meson and observation of $D^0\to K^-\pi^+e^+e^-$