Search for Lepton Flavor Violation inK+Decays into a Charged Pion and Two Leptons

A search for lepton flavor violating decays, $K^{+}\to {\mu }^{+}{\mu }^{+}{\pi }^{-}$, $K^{+}\to e^{+}{e}^{+}{\pi }^{-}$, $K^{+}\to {\pi }^{+}{e}^{+}{\mu }^{-}$, $K^{+}\to {\mu }^{+}{e}^{+}{\pi }^{-}$, and ${\pi }^0\to e^{+}{\mu }^{-}$, was performed using the data collected in Experiment E865 at the Brookhaven Alternating Gradient Synchrotron. No signal was found in any of the decay modes. At the $90\%$ confidence level, the branching ratios are less than $3.0\times {10}^{-9\mathrm{}}$, $6.4\times {10}^{-10\mathrm{}}$, $5.2\times {10}^{-10\mathrm{}}$, $5.0\times {10}^{-10\mathrm{}}$, and $3.4\times {10}^{-9\mathrm{}}$, respectively.