Precise determination of the Z resonance parameters at LEP: “Zedometry”

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This final analysis of hadronic and leptonic cross-sections and of leptonic forward-backward asymmetries in \({\mathrme}^+{\mathrme}^-\) collisions with the OPAL detector makes use of the full LEP 1 data sample comprising \(161 \mathrm{pb}^{-1}\) of integrated luminosity and \(4.5\times10^6\) selected Z decays. An interpretation of the data in terms of contributions from pure Z exchange and from \(\gamma/\)Z interference allows the parameters of the Z resonance to be determined in a model-independent way. Our results are in good agreement with lepton universality and consistent with the vector and axial-vector couplings predicted in the Standard Model. A fit to the complete dataset yields the fundamental Z resonance parameters: \(m_{\mathrm{Z}} = (91.1852 \pm 0.0030)\) GeV, \(\Gamma_{\mathrm{Z}} = (2.4948 \pm 0.0041)\) GeV, \(\sigma^0_{\mathrm{h}} = (41.501 \pm 0.055)\) nb, \(R_{\ell} = 20.823 \pm 0.044\), and \(A_{\mathrm{FB}}^{0,\ell} = 0.0145 \pm 0.0017\). Transforming these parameters gives a measurement of the ratio between the decay width into invisible particles and the width to a single species of charged lepton, \(\Gamma_{\mathrm{inv}}/\Gamma_{\ell\ell} = 5.942 \pm 0.027\). Attributing the entire invisible width to neutrino decays and assuming the Standard Model couplings for neutrinos, this translates into a measurement of the effective number of light neutrino species, \(N_{\nu} = 2.984 \pm 0.013\). Interpreting the data within the context of the Standard Model allows the mass of the top quark, \(m_{\mathrm{t}} = (162 ^{+29}_{-16})\) GeV, to be determined through its influence on radiative corrections. Alternatively, utilising the direct external measurement of \(m_{\mathrm{t}}\) as an additional constraint leads to a measurement of the strong coupling constant and the mass of the Higgs boson: \(\alpha_{\mathrm{s}}(m_{\mathrm{Z}}) = 0.127 \pm 0.005\) and \(m_{\mathrm{H}} = (390^{+750}_{-280})\) GeV.