We investigate the parton distribution function (PDF) uncertainty in the measurement of the effective weak mixing angle $sin^2theta_{text{eff}}^{ell}$ at the CERN Large Hadron Collider (LHC). The PDF-induced uncertainty is large in the proton-proton collisions at the LHC due to the dilution effect. The measurement of the Drell-Yan forward-backward asymmetry ($A_{FB}$) at the LHC can be used to reduce the PDF uncertainty in the $sin^2theta_{text{eff}}^{ell}$ measurement. However, when including the full mass range of lepton pairs in the $A_{FB}$ data analysis, the correlation between the PDF updating procedure and the $sin^2theta_{text{eff}}^{ell}$ extraction leads to a sizable bias in the obtained $sin^2theta_{text{eff}}^{ell}$ value. From our studies, we find that the bias can be significantly reduced by removing Drell-Yan events with invariant mass around the $Z$ pole region, while most of the sensitivity in reducing the PDF uncertainty remains. Furthermore, the lepton charge asymmetry in the $W$ boson events as a function of the rapidity of the charged leptons, $A_pm(eta_ell)$, is known to be another observable which can be used to reduce the PDF uncertainty in the $sin^2theta_{text{eff}}^{ell}$ measurement. The constraint from $A_pm(eta_ell)$ is complementary to that from the $A_{FB}$, thus no bias affects the $sin^2theta_{text{eff}}^{ell}$ extraction. The studies are performed using the Error PDF Updating Method Package ({sc ePump}), which is based on the Hessian updating methods. In this article, the CT14HERA2 PDF set is used as an example.
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