Reduction of PDF uncertainty in the measurement of the weak mixing angle at the ATLAS experiment

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.