First Measurement of the Left-Right Charge Asymmetry in Hadronic $\mathit{Z}$ Boson Decays and a New Determination of ${\sin }^2{\mathit{\theta }}_{\mathit{W}}^{\mathrm{eff}}$

We present the first measurement of the left-right charge asymmetry $A_Q^{\mathrm{obs}}$ in hadronic $Z$ boson decays. This was performed at $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=91.27\mathrm{}\mathrm{GeV}$ with the SLD at the SLAC Linear Collider with a polarized electron beam. Using 89 838 events we obtain $A_Q^{\mathrm{obs}}=0.225\mathrm{}\pm 0.056\pm 0.019$, which leads to a measurement of the electron left-right asymmetry parameter, $A_e=0.162\mathrm{}\pm 0.041\pm 0.014$, and ${sin}^2{\theta }_W^{\mathrm{eff}}=0.2297\mathrm{}\pm 0.0052\pm 0.0018$. Also, the $A_Q^{\mathrm{obs}}$ measurement combined with the left-right cross section asymmetry determines $A_e$ independent of the value of the electron-beam polarization.