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

TL;DR

This paper explores methods to reduce PDF uncertainties in measuring the weak mixing angle at the LHC, focusing on the use of $A_{FB}$ and $A_ ext{charge}$ observables and employing the ePump PDF updating tool.

Contribution

It demonstrates that removing Z pole events and using lepton charge asymmetry can significantly reduce PDF-induced bias and uncertainty in the measurement.

Findings

Removing Z pole events reduces bias in $ heta_{eff}$ measurement.

Lepton charge asymmetry provides a bias-free constraint on PDFs.

Combined use of $A_{FB}$ and $A_ ext{charge}$ improves measurement precision.

Abstract

We investigate the parton distribution function (PDF) uncertainty in the measurement of the effective weak mixing angle $\sin^2\theta_{\text{eff}}^{\ell}$ 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 $\sin^2\theta_{\text{eff}}^{\ell}$ 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 $\sin^2\theta_{\text{eff}}^{\ell}$ extraction leads to a sizable bias in the obtained $\sin^2\theta_{\text{eff}}^{\ell}$ 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 $\sin^2\theta_{\text{eff}}^{\ell}$ measurement. The constraint from $A_\pm(\eta_\ell)$ is complementary to that from the $A_{FB}$, thus no bias affects the $\sin^2\theta_{\text{eff}}^{\ell}$ 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.