Standard Model Decays of Tau into Three Charged Leptons

Analytic expressions are given for the $\tau$ decays into three charged leptons, $\tau\rta \ell\ell\overline \ell\nu_\tau\overline \nu_\ell$, where the $\ell$ are combinations of electrons and muons, and for the radiative decays $\tau\rta \gamma\ell\nu_\tau\overline \nu_\ell$. The branching ratios are sensitive functions of whether the final state $\ell$ are muons or electrons.