Precise Determination of the Weak Mixing Angle from a measurement of ALR in e+e- -> Z0

In the 1993 SLC/SLD run, the SLD recorded 50,000 $\z0$ events produced by the collision of longitudinally polarized electrons on unpolarized positrons at a center-of-mass energy of 91.26 GeV. The luminosity-weighted average polarization of the SLC electron beam was (63.0$\pm$1.1)\%. We measure the left-right cross-section asymmetry in $\z0$ boson production, $\alr$, to be 0.1628$\pm$0.0071(stat.)$\pm$0.0028(syst.) which determines the effective weak mixing angle to be $\swein=0.2292\pm0.0009({\rm stat.})\pm0.0004({\rm syst.}).$

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