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Abstract

We review the current status and techniques used in precision measurements of the effective leptonic weak mixing angle $\sin^2\theta^\ell_{\rm eff}$ (a fundamental parameter of the Standard Model (SM)) in the region of the Z pole with emphasis on hadron colliders. We also build on these techniques to extract the most precise single measurement to date of $\sin^2\theta^\ell_{\rm eff}$ from a new analysis of the published forward-backward asymmetry ($A_{\rm FB}$) in Drell-Yan dielpton production in proton-proton collisions at a center of mass energy of 13 TeV measured by the CMS collaboration at the large hadron collider. The uncertainty in $\sin^2\theta^\ell_{\rm eff}$ published by CMS is dominated by uncertainties in Parton Distribution Functions (PDFs), which are reduced by PDF profiling using the dilepton mass dependence of $A_{\rm FB}$. Our new extraction of $\sin^2\theta^\ell_{\rm eff}$ from the CMS values of $A_{\rm FB}$ includes profiling with additional new CMS measurements of the $W$-boson decay lepton asymmetry, and W/Z cross section ratio at 13 TeV. We obtain the most precise single measurement of $\sin^2\theta^\ell_{\rm eff}$ to date of 0.23156$\pm$0.00024, which is in excellent agreement with the SM prediction of 0.23161$\pm$0.00004. We also discuss outlook for future measurements at the LHC including more precise measurements of $\sin^2\theta^\ell_{\rm eff}$, a measurement of $\sin^2\theta^\ell_{\rm eff}$ for b-quarks in the initial state, and a measurement of the running of $\sin^2\theta^{\overline{\rm MS}}(\mu)$ up to 3 TeV.