Measurement of the Tau Polarisation at LEP

The polarisation of $\tau$ 's produced in Z decay is measured using 160 pb $^{-1}$ of data accumulated at LEP by the ALEPH detector between 1990 and 1995. The variation of the polarisation with polar angle yields the two parameters ${\cal A}_e = 0.1504 \pm 0.0068 $ and ${\cal A}_{\tau} = 0.1451 \pm 0.0059$ which are consistent with the hypothesis of e- $\tau$ universality. Assuming universality, the value ${\cal A}_{e\mbox{-}\tau} = 0.1474 \pm 0.0045$ is obtained from which the effective weak mixing angle $\sin^2{\theta_{\mathrm{W}}^{\mathrm{eff}}} =0.23147 \pm 0.00057 $ is derived.