Measurements of cross sections and forward-backward asymmetries at the Z resonance and determination of electroweak parameters

We report on measurements of hadronic and leptonic cross sections and leptonic forward-backward asymmetries performed with the L3 detector in the years $1993-95$.A total luminosity of 103 pb$^{-1}$ was collected at centre-of-mass energies $\sqrt{s} \approx m_\mathrm{Z}$ and $\sqrt{s} \approx m_\mathrm{Z} \pm 1.8$ GeVwhich corresponds to 2.5 million hadronic and 245 thousand leptonic events selected.These data lead to a significantly improved determination of Z parameters.From the total cross sections, combined with our measurements in $1990-92$,we obtain the final results:%%%\begin{eqnarr ay*} m_\mathrm{Z} = 91189.8 \pm 3.1\ \mathrm{MeV} \, , & & \Gamma_\mathrm{Z} = 2502.4 \pm 4.2\ \mathrm{MeV} \, , \\ \Gamma_\mathrm{had} = 1741.1 \pm 3.8\ \mathrm{MeV} \, , & & \Gamma_\ell = 84.14 \pm 0.17\ \mathrm{MeV} \,. \label{eq:Zpara_abstract}\end{eqnarray*}%%%An invisible width of $\Gamma_\mathrm{inv} = 499.1 \pm 2.9$ MeV is derived which in the Standard Model yields for the numberof light neutrino species $N_\nu = 2.978 \pm 0.014$.Adding our results on the leptonic forward-backward asymmetries and thetau polarisation, the effective vector and axial-vector coupling constants of the neutral weak current to charged leptons are determined to be $\bar{g}_{\mathrm{V}}^\ell = -0.0397\pm 0.0017$ and $\bar{g}_{\mathrm{A}}^\ell = -0.50153 \pm 0.00053$.Including our measurements of the Z $\rightarrow \mathrm{b}\bar{\mathrm{b}}$ forward-backward and quark charge asymmetries a value for the effective electroweakmixing angle of $\sin^2\!\overline{\theta}_{\mathrm{W}} = 0.23093 \pm 0.00066$ is derived. All these measurements are in good agreement with the Standard Modelof electroweak interactions.Using all our measurements of electroweak observables an upper limit on the mass of the Standard Model Higgs boson of $m_\mathrm{H} 133 $ GeV is set at 95\% confidence level.