Abstract: Drell-Yan lepton pairs are produced in the process p¯p?µ+µ-+X through an intermediate ?*/Zboson. The forward-backward asymmetry in the polar-angle distribution of the µ- as a function of the invariant mass of the µ+µ- pair is used to obtain the effective leptonic determination sin2?lepteff of the electroweak-mixing parameter sin2?W, from which the value of sin2?W is derived assuming the standard model. The measurement sample, recorded by the Collider Detector at Fermilab (CDF), corresponds to 9.2??fb-1 of integrated luminosity from p¯p collisions at a center-of-momentum energy of 1.96 TeV, and is the full CDF Run II data set. The value of sin2?lepteff is found to be 0.2315±0.0010, where statistical and systematic uncertainties are combined in quadrature. When interpreted within the context of the standard model using the on-shell renormalization scheme, where sin2?W=1-M2W/M2Z, the measurement yields sin2?W=0.2233±0.0009, or equivalently a W-boson mass of 80.365±0.047??GeV/c2. The value of the W-boson mass is in agreement with previous determinations in electron-positron collisions and at the Tevatron collider.

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