Tau Decays into Three Charged Leptons and Two Neutrinos

We search for the radiative leptonic tau decays $\tau \to {\mathrm{ee}}^{+}{e}^{-}{\nu }_{\tau }{\nu }_e$ and $\tau \to \mu e^{+}{e}^{-}{\nu }_{\tau }{\nu }_{\mu }$ using $3.60{\mathrm{fb}}^{-1\mathrm{}}$ of data collected by the CLEO-II experiment at the Cornell Electron Storage Ring. We present a first observation of the $\tau \to {\mathrm{ee}}^{+}{e}^{-}{\nu }_{\tau }{\nu }_e$ process. For this channel we measure the branching fraction $B(\tau \to {\mathrm{ee}}^{+}{e}^{-}{\nu }_{\tau }{\nu }_e)=\left({2.7}_{-1.1-0.4-0.3\mathrm{}}^{+1.5+0.4+0.1\mathrm{}}\right)\times {10}^{-5\mathrm{}}$. An upper limit is established for the second channel: $B(\tau \to \mu e^{+}{e}^{-}{\nu }_{\tau }{\nu }_{\mu })<3.2\mathrm{}\times {10}^{-5\mathrm{}}$ at 90% C.L. Both results are consistent with the rates expected from standard model predictions.