We present a precise measurement of the left-right cross section asymmetry ($A_{\mathrm{LR}}$) for $Z$ boson production by $e^{+}{e}^{-}$ collisions. The measurement was performed at a center-of-mass energy of 91.26 GeV with the SLD detector at the SLAC Linear Collider (SLC). The luminosity-weighted average polarization of the SLC electron beam was (63.0 ± 1.1)%. Using a sample of 49 392 $Z$ decays, we measure $A_{\mathrm{LR}}$ to be 0.1628 ± 0.0071 (stat) ± 0.0028 (syst) which determines the effective weak mixing angle to be ${sin}^2{\theta }_W^{\mathrm{eff}}=0.2292\mathrm{}\pm 0.0009\left(\mathrm{stat}\right)\pm 0.0004\left(\mathrm{syst}\right)$.

• Received 31 March 1994

DOI:https://doi.org/10.1103/PhysRevLett.73.25