Electronic branching ratio of the $\tau$ lepton

Using data accumulated by the CLEO I detector operating at the Cornell Electron Storage Ring, we have measured the ratio $R=\frac{\Gamma (\tau \to e{\overline{\nu }}_e{\nu }_{\tau })}{{\Gamma }_1}$ where ${\Gamma }_1$ is the $\tau$ decay rate to final states with one charged particle. We find $R=0.2231\mathrm{}\pm 0.0044\pm 0.0073$ where the first error is statistical and the second is systematic. Together with the measured topological one-charged-particle branching fraction, this yields the branching fraction of the $\tau$ lepton to electrons, $B_e=0.192\mathrm{}\pm 0.004\pm 0.006$.