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

Abstract From a sample of 3308 e + e − → τ + τ − events with an estimated background of 1.9%, we find 964 τ → e ν ν , 903 τ → μν ν , 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 → e ν ν ) = 17.4 ± 0.5 ( stat ) ± 0.4 ( sys )% , B(τ → μν ν ) = 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 sin 2 θ W = 0.237 ± 0.009 , with no ambiguity introduced by the relative signs of ν and α.