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Drell-Yan lepton pairs are produced in the process $p\bar{p} \rightarrow\mu^+\mu^- + X$ through an intermediate $\gamma^*/Z$ boson. Theforward-backward asymmetry in the polar-angle distribution of the $\mu^-$ as afunction of the invariant mass of the $\mu^+\mu^-$ pair is used to obtain theeffective leptonic determination $\sin^2 \theta^{lept}_{eff}$ of theelectroweak-mixing parameter $\sin^2 \theta_W$, from which the value of $\sin^2\theta_W$ is derived assuming the standard model. The measurement sample,recorded by the Collider Detector at Fermilab (CDF), corresponds to 9.2 fb-1 ofintegrated luminosity from $p\bar{p}$ collisions at a center-of-momentum energyof 1.96 TeV, and is the full CDF Run II data set. The value of $\sin^2\theta^{lept}_{eff}$ is found to be 0.2315 +- 0.0010, where statistical andsystematic uncertainties are combined in quadrature. When interpreted withinthe context of the standard model using the on-shell renormalization scheme,where $\sin^2 \theta_W = 1 - M_W^2/M_Z^2$, the measurement yields $\sin^2\theta_W$ = 0.2233 +- 0.0009, or equivalently a W-boson mass of 80.365 +- 0.047GeV/c^2. The value of the W-boson mass is in agreement with previousdeterminations in electron-positron collisions and at the Tevatron collider.

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

Indirect measurement of $\sin^2 \theta_W$ (or $M_W$) using $\mu^+\mu^-$  pairs from $\gamma^*/Z$ bosons produced in $p\bar{p}$ collisions at a  center-of-momentum energy of 1.96 TeV