a Measurement of the Polarization of Tau Leptons in Z Decays with the l3 Detector at Lep.

We report on the measurement of the polarization of tau leptons with the L3 detector. Tau lepton pairs were produced in electron-positron collisions in the Large Electron-Positron storage ring (LEP), located at the European Center for Particle Physics (CERN). The data sample consists of an integrated luminosity of 17.6 pb^ {-1} collected during the 1990 and 1991 collider runs, with center of mass energies ranging from 88 to 94 GeV. The polarization is measured to be { cal A}_{rm POL}(tau)= -0.132+/- 0.026+/- 0.021, where the quoted errors are statistical and systematic, respectively. From this asymmetry, we extract a measurement of the ratio of the effective vector and axial-vector couplings of the tau lepton to the weak neutral current of rm(V _tau/A_tau)_{eff}=0.068 +/- 0.017, confirming that parity is violated in weak neutral currents. In the Standard Model, this corresponds to a value for the effective weak mixing parameter of rm sin^2theta_sp{W }{eff}=0.2330+/- 0.0043..