Precision Measurement ofsin2θWfrom Semileptonic Neutrino Scattering

The ratio $R_{\nu }$ of the neutral- to charged-current cross sections of neutrinos in iron has been measured in an exposure of the CERN-Dortmund-Heidelberg-Saclay neutrino detector to a 160-GeV/c neutrino narrow-band beam at the CERN Super Proton Synchrotron. The result is $R_{\nu }=0.3072\mathrm{}\pm 0.0025\left(\mathrm{stat}\right)\pm 0.0020\left(\mathrm{syst}\right)$, for hadronic energy greater than 10 GeV. The electroweak mixing parameter is ${sin}^2{\theta }_W=0.225\mathrm{}\pm 0.005\left(\mathrm{expt}\right)\pm 0.003\left(\mathrm{theor}\right)+0.013(m_c-1.5\mathrm{} \frac{\mathrm{GeV}}{c^2})$, where $m_c$ is the charm-quark mass.