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At the Fermilab Tevatron proton-antiproton ($p\bar{p}$) collider, Drell-Yanlepton pairs are produced in the process $p \bar{p} \rightarrow e^+e^- + X$through an intermediate $\gamma^*/Z$ boson. The forward-backward asymmetry inthe polar-angle distribution of the $e^-$ as a function of the $e^+e^-$-pairmass is used to obtain $\sin^2\theta^{\rm lept}_{\rm eff}$, the effectiveleptonic determination of the electroweak-mixing parameter $\sin^2\theta_W$.The measurement sample, recorded by the Collider Detector at Fermilab (CDF),corresponds to 9.4~fb$^{-1}$ of integrated luminosity from $p\bar{p}$collisions at a center-of-momentum energy of 1.96 TeV, and is the full CDF RunII data set. The value of $\sin^2\theta^{\rm lept}_{\rm eff}$ is found to be$0.23248 \pm 0.00053$. The combination with the previous CDF measurement basedon $\mu^+\mu^-$ pairs yields $\sin^2\theta^{\rm lept}_{\rm eff} = 0.23221 \pm0.00046$. This result, when interpreted within the specified context of thestandard model assuming $\sin^2 \theta_W = 1 - M_W^2/M_Z^2$ and that the $W$-and $Z$-boson masses are on-shell, yields $\sin^2\theta_W = 0.22400 \pm0.00045$, or equivalently a $W$-boson mass of $80.328 \pm 0.024 \;{\rmGeV}/c^2$.

physical review. d/physical review. d.

Measurement of $\sin^2\theta^{\rm lept}_{\rm eff}$ using $e^+e^-$ pairs  from $\gamma^*/Z$ bosons produced in $p\bar{p}$ collisions at a  center-of-momentum energy of 1.96 TeV