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

Abstract

At the Fermilab Tevatron proton-antiproton ($p\bar{p}$) collider, Drell-Yan lepton pairs are produced in the process $p\bar{p}\to e^{+}{e}^{-}+X$ through an intermediate $γ^*/Z$ boson. The forward-backward asymmetry in the polar-angle distribution of the $e^{-}$ as a function of the $e^{+}{e}^{-}$-pair mass is used to obtain ${\sin }^2\hat{I}{¸}_{\mathrm{eff}}^{\mathrm{lept}}$, the effective leptonic determination of the electroweak-mixing parameter ${\sin }^2\hat{I}{¸}_W$. 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 Run II data set. The value of ${\sin }^2\hat{I}{¸}_{\mathrm{eff}}^{\mathrm{lept}}$ is found to be $0.23248\pm 0.00053$. The combination with the previous CDF measurement based on $\hat{I}{¼}^{+}\hat{I}{¼}^{-}$ pairs yields ${\sin }^2\hat{I}{¸}_{\mathrm{eff}}^{\mathrm{lept}}=0.23221\pm 0.00046$. This result, when interpreted within the specified context of the standard model assuming ${\sin }^2\hat{I}{¸}_W=1-M_W^2/M_Z^2$ and that the $W$- and $Z$-boson masses are on-shell, yields ${\sin }^2\hat{I}{¸}_W=0.22400\pm 0.00045$, or equivalently a $W$-boson mass of $80.328\pm 0.024\mathrm{GeV}/c^2$.