We present a new measurement of the left-right cross section asymmetry $\left(A_{\mathrm{LR}}\right)$ for $Z$ boson production by $e^{+}{e}^{-}$ collisions. The measurement was performed at a center-of-mass energy of 91.28 GeV with the SLD detector at the SLAC Linear Collider (SLC). The luminosity-weighted average polarization of the SLC electron beam was $(77.23\pm 0.52)\%$. Using a sample of 93 644 $Z$ decays, we measure the pole value of the asymmetry, $A_{\mathrm{LR}}^0$, to be $0.1512\pm 0.0042\left(\mathrm{stat}\right)\pm 0.0011\left(\mathrm{syst}\right)$, which is equivalent to an effective weak mixing angle of $\sin {}^2{\theta }_W^{\mathrm{eff}}=0.231\mathrm{}00\pm 0.00054\left(\mathrm{stat}\right)\pm 0.00014\left(\mathrm{syst}\right)$.

• Received 21 November 1996

DOI:https://doi.org/10.1103/PhysRevLett.78.2075