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We measure the mass dependence of the forward-backward charge asymmetry in157,553 $p\bar{p} \rightarrow Z/\gamma^{*} \rightarrow e^+e^-$ interactions,corresponding to 5.0 fb$^{-1}$ of integrated luminosity collected by the D0experiment at the Fermilab Tevatron Collider at $\sqrt{s}=1.96$ TeV. Theeffective weak mixing angle ($\sin^2\theta_{eff}^{lept}$) from this processinvolving predominantly the first generation of quarks is extracted as$\sin^2\theta_{eff}^{lept} = 0.2309 \pm 0.0008 ({stat.}) \pm 0.0006 ({syst.})$.We also present the most precise direct measurement of the vector andaxial-vector couplings of $u$ and $d$ quarks to the $Z$ boson.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Measurement of sin^2\theta_{eff}^{lept} and Z-light quark couplings  using the forward-backward charge asymmetry in p\bar{p} -> Z/\gamma^{*} ->  e^{+}e^{-} events with L=5.0 fb^{-1} at \sqrt{s}=1.96 TeV