Precise Measurement of the Left-Right Cross Section Asymmetry in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Z</mml:mi></mml:math>Boson Production by<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>Collisions

We present a precise measurement of the left-right cross section asymmetry (${A}_{\mathrm{LR}}$) for $Z$ boson production by ${e}^{+}{e}^{\ensuremath{-}}$ 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 \ifmmode\pm\else\textpm\fi{} 1.1)%. Using a sample of 49 392 $Z$ decays, we measure ${A}_{\mathrm{LR}}$ to be 0.1628 \ifmmode\pm\else\textpm\fi{} 0.0071 (stat) \ifmmode\pm\else\textpm\fi{} 0.0028 (syst) which determines the effective weak mixing angle to be ${sin}^{2}{\ensuremath{\theta}}_{W}^{\mathrm{eff}}=0.2292\ifmmode\pm\else\textpm\fi{}0.0009(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.0004(\mathrm{syst})$.