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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