Test of the CP invariance in the decay Z0 →τanti τand weak dipole moment determination of the τlepton

Using 19742 Z0→τ anti τ decays, accumulated in 1991 and 1992 with the OPAL-detector at LEP, a direct test of CP-invariance in the neutral current reaction e+e-→τ+τ- is performed by measuring CP-odd observables. They are proportional to the weak dipole moment of the τ-lepton. Employing a new method based on optimal CP observables constructed from the τ flight and spin directions more sensitive measurements on the real and - for the first time - the imaginary part of the weak dipole moment with highest possible signal to noise ratio is obtained. No evidence for a non-zero expectation value of the considered observables and hence for CP-violation is observed. An upper limit on the weak dipole moment of vertical stroke Re(dτω)vertical stroke <1.2x10-17 e cm and vertical stroke Im(dτω)vertical stroke <4.0x10-17 e cm with 95% confidence level is given. (orig.)