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 ${\cal A}_{e{-}\tau} = 0.1474 \pm 0.0045$ is obtained from which the effective weak mixing angle $\sin^2 {\theta_{\mathrm{W}}^{\mathrm{eff}}} =0.23147 \pm 0.00057 $ is derived.
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Using the 18.8 pb −1 of data accumulated at LEP in 1990 and 1991 with the ALEPH detector, a direct test of neutral current CP -invariance is performed by a search for CP -odd correlations in Z decays to τ pairs where both τ decay modes are identified. No evidence for CP -violation is observed. The weak dipole moment of the τ has been measured to be d τ ( m Z ) = (1.3 ± 1.4 ± 0.1) × 10 −17 e ·cm which results in an upper limit on the weak dipole moment of | d τ ( m Z )| ⩽ 3.7 × 10 −17 e ·cm with 95% confidence level.
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