Measurements of the tau-polarization in Z(0) decays

A sample of Z(0) --> tau(+)tau(-) events observed in the DELPHI detector at LEP in 1991 and 1992 is analysed to measure the tau polarisation in the exclusive decay channels e nu ($) over bar nu, mu nu ($) over bar nu, pi nu, rho nu and a(l) nu. The tau polarisation is also measured with an inclusive hadronic analysis which benefits from a higher efficiency and a better systematic precision than the use of the exclusive decay modes. The results have been combined with those published on the 1990 data. A measurement of the tau polarisation as a function of production angle yields the values for the mean tau polarisation [P-tau] = -0.148 +/- 0.022 and for the Z(0) polarisation P-z = -0.136 +/- 0.027. These results are used to determine the ratio of vector to axial-vector effective couplings for taus ($) over bar upsilon(tau)/($) over bar a(tau) = 0.074 +/- 0.011 and for electrons ($) over bar upsilon(e)/($) over bar a(e) = 0.068 +/- 0.014, compatible with e-tau universality. With the assumption of lepton universality, the ratio of vector to axial-vector effective couplings for leptons ($) over bar upsilon(l)/($) over bar a(l) = 0.072 +/- 0.008 is obtained, implying a value of the effective weak mixing angle sin(2) theta(eff)(lept) = 0.2320 +/- 0.0021.