Measurement of the forward-backward charge asymmetry and extraction of $sin^2Theta^{eff}_W$ in $p\bar{p} \to Z/\gamma^{}+X \to e^+e^-+X$ events produced at $\sqrt{s}=1.96$ TeV

We present a measurement of the forward-backward charge asymmetry ($A_{FB}$) in $p\bar{p} \to Z/\gamma^{*}+X \to e^+e^-+X$ events at a center-of-mass energy of 1.96 TeV using 1.1 fb$^{-1}$ of data collected with the D0 detector at the Fermilab Tevatron collider. $A_{FB}$ is measured as a function of the invariant mass of the electron-positron pair, and found to be consistent with the standard model prediction. We use the $A_{FB}$ measurement to extract the effective weak mixing angle $sin^2Theta^{eff}_W = 0.2327 \pm 0.0018 (stat.) \pm 0.0006 (syst.)$.