Observation of Radiative Leptonic Decay of the Tau Lepton

Using $4.68{\mathrm{fb}}^{-1\mathrm{}}$ of $e^{+}{e}^{-}$ annihilation data collected with the CLEO II detector at the Cornell Electron Storage Ring, we have studied $\tau$ radiative decays ${\tau }^{-}\to {\nu }_{\tau }{\mu }^{-}{\overline{\nu }}_{\mu }\gamma$ and ${\tau }^{-}\to {\nu }_{\tau }{e}^{-}{\overline{\nu }}_e\gamma$. For a 10 MeV minimum photon energy in the $\tau$ rest frame, the branching fraction for radiative $\tau$ decay to a muon or electron is measured to be $(3.61\pm 0.16\pm 0.35)\times {10}^{-3\mathrm{}}$ or $(1.75\pm 0.06\pm 0.17)\times {10}^{-2\mathrm{}}$, respectively. The branching fractions are in agreement with standard model theoretical predictions.