Measurement of branching ratios and τ polarization from τ→eνν^-,τ→μνν^-,andτ→π(K)ν decays at LEP

From a sample of 3308 e⁺e^- → τ⁺τ^- events with an estimated background of 1.9%, we find 964 τ → eνν, 903 τ → μνν, and 309 τ → π(K)ν candidates. Efficiency and background estimates determined from both Monte Carlo and control sample studies yield the following branching ratios: B(τ → eνν) = 17.4 ± 0.5 (stat) ± 0.4 (sys)%, B(τ → μνν) = 16.8 ± 0.5 ± 0.4%, and B(τ → π(K)ν) = 12.1 ± 0.7 ± 0.5%. These values are in good agreement with previous measurements. The measured lepton branching ratios, when combined with the world-average measured value for the τ lifetime, yield a ratio of the τ Fermi coupling constant to that of the lighter leptons given by G_τ/G_e,μ = 0.92 ± 0.04, where it is assumed G_e = G_μ ≡ G_e,μ. The average τ polarization at the Z° resonance is measured to be -0.01±0.09 from an analysis of the momentum spectra of the electron, muon, and pion candidates, implying that the ratio of vector to axial vector couplings of the τ to the Z° is ν_τ/α_τ = 0.01 ± 0.04. The measurements of the average polarizations in the forward and backward hemispheres lead to the efficiency-corrected, forward-backward polarization asymmetry A^FB_pol = -0.22 ± 0.10, implying for the electron couplings to the Z° the ratio ν_e/α_e = 0.15±0.07. Since these values for the tau and electron couplings are consistent with one another, we assume lepton universality to derive ν/α = 0.05 ± 0.04 and a value for the weak mixing angle of sin²θ_W = 0.237 ± 0.009, with no ambiguity introduced by the relative signs of ν and α.