Measurement of the Weak Dipole Moments of the $\tau$ Lepton

Using the data collected by the L3 experiment at LEP from 1991 to 1995 at energies around the $\Zo$ mass, a measurement of the weak anomalous magnetic dipole moment, $a^w_{\tau}$,~ and of the weak electric dipole moment, $d^w_{\tau}$, of the $\tau$ lepton is performed. These quantities are obtained from angular distributions in $e^{+}e^{-}\rightarrow\tau^{+}\tau^{-} \rightarrow h^{+} \bar{\nu}_{\tau} h^{-} \nu_{\tau}$, where $h$ is a $\pi$ or a $\rho$. The results are: $Re(a^w_{\tau}) = (0.0 \pm 1.6 \pm 1.6) \times 10^{-3}$, $Im(a^w_{\tau}) = (-1.0 \pm 3.6 \pm 3.7) \times 10^{-3}$ and $d^w_{\tau} = (-0.44 \pm 0.88 \pm 0.94) \times 10^{-17} \rm{e \cdot cm}$. This is the first direct measurement of $a^w_{\tau}$