Search for neutrinoless $\tau$ decays involving the $K_S^0$ meson

We have searched for lepton flavor violating decays of the $\tau$ lepton with one or two $K_S^0$ mesons in the final state. The data used in the search were collected with the CLEO II and II.V detectors at the Cornell Electron Storage Ring (CESR) and correspond to an integrated luminosity of $13.9{\mathrm{fb}}^{-1}$ at the ${\rm Y}\mathrm{}\left(4S\right)\mathrm{}$ resonance. No evidence for signals were found; therefore, we have set 90% confidence level (C.L.) upper limits on the branching fractions $\mathcal{B}({\tau }^{-}\to e^{-}{K}_S^0)<\mathrm{}9.1\mathrm{}\times {10}^{-7},$ $\mathcal{B}({\tau }^{-}\to {\mu }^{-}{K}_S^0)<\mathrm{}9.5\mathrm{}\times {10}^{-7},$ $\mathcal{B}({\tau }^{-}\to e^{-}{K}_S^0{K}_S^0)<\mathrm{}2.2\mathrm{}\times {10}^{-6},$ and $\mathcal{B}({\tau }^{-}\to {\mu }^{-}{K}_S^0{K}_S^0)<\mathrm{}3.4\mathrm{}\times {10}^{-6}.$ These represent significantly improved upper limits on the two-body decays and first upper limits on the three-body decays.