We present the first measurement of the left-right cross section asymmetry (${\mathit{A}}_{\mathit{L}\mathit{R}}$) for Z boson production by ${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{-}}$ collisions. The measurement was performed at a center-of-mass energy of 91.55 GeV with the SLD detector at the SLAC Linear Collider which utilized a longitudinally polarized electron beam. The average beam polarization was (22.4±0.6)%. Using a sample of 10 224 Z decays, we measure ${\mathit{A}}_{\mathit{L}\mathit{R}}$ to be 0.100±0.044(stat)±0.004(syst), which determines the effective weak mixing angle to be ${\sin }^2$${\mathrm{\theta }}_{\mathit{W}}^{\mathit{e}\mathit{f}\mathit{f}}$=0.2378 ±0.0056(stat)±0.0005(syst).

• Received 15 January 1993

DOI:https://doi.org/10.1103/PhysRevLett.70.2515