Analysis of the $\tau$ Polarization and its Forward-Backward Asymmetry on the $Z^{0}$

This thesis describes a new a measurement of the tau lepton polarization and its forward-backward asymmetry at the Z resonance using the OPAL detector. This measurement is based on analyses of the tau->electron, muon and pion (Kaon) decays from a sample of 30663 tau-pair events collected in the polar angle range of Abs(cos(theta)) <0.68 during the 1990-1992 data taking period. Taking then the Standard Model with the V-A structure of the tau lepton decay, we measure the average tau polarization to be <p_tau>=(-13.5+/-2.9+/-2.2)% and the tau polarization forward-backward asymmetry to be AFBpol=(-11.0+/-3.5+/-0.5)% where the first error is statistical and the second systematic. Combining these figures with the OPAL <p_tau> and AFBpol measured with the tau->rho channel we get an average tau polarization, <p_tau>=(-14.9+/-1.9+/-1.3)% and for the asymmetry in the polarization, AFBpol=(-8.9+/-2.2+/-0.9)% . These results are consistent with lepton universality. Combining the two results we obtain for the electroweak mixing angle the value sin^2(theta_W)=0.2331+/-0.0023 within the context of the Standard Model, where the error includes both statistical and systematic uncertainties.