We present a measurement of the left-right cross-section asymmetry ( $A_{\mathrm{LR}}$) for $Z$ boson production by $e^{+}{e}^{-}$ collisions. The measurement includes the final data taken with the SLD detector at the SLAC Linear Collider during the period 1996–1998. Using a sample of 383 487 $Z$ decays collected during the 1996–1998 runs we measure the pole value of the asymmetry, $A_{\mathrm{LR}}^0$, to be $0.15056\pm 0.00239$ which is equivalent to an effective weak mixing angle of ${sin}^2{\theta }_W^{\mathrm{eff}}=0.231\mathrm{}07\pm 0.00030$. Our result for the complete 1992–1998 data set comprising approximately 537 000 $Z$ decays is ${sin}^2{\theta }_W^{\mathrm{eff}}=0.230\mathrm{}97\pm 0.00027$.

• Received 17 April 2000

DOI:https://doi.org/10.1103/PhysRevLett.84.5945