Summary of the Precision Measurements of the Electroweak Mixing Angle in the Region of the Z pole

This contribution presents an overview of an improved extraction of the effective leptonic weak mixing angle, $\sin^2θ^\ell_{\mathrm{eff}}$, based on the published CMS measurement of the forward-backward asymmetry in Drell-Yan events at 13 TeV [1]. While the original CMS analysis [2] achieved a significant reduction in experimental uncertainties, its overall precision remains limited by residual uncertainties in the parton distribution functions (PDFs). This proceeding highlights the impact of incorporating complementary CMS measurements that probe different combinations of parton densities, thereby providing additional PDF constraints beyond those obtained from the asymmetry measurement alone. The improved analysis leads to a substantially reduced total uncertainty, yielding $\sin^2θ^\ell_{\mathrm{eff}} = 0.23156\pm0.00024$. This result is consistent with the Standard Model prediction and represents the most precise single determination of this parameter to date.

💡 Research Summary

This paper presents an updated determination of the effective leptonic weak mixing angle, sin²θ_eff^ℓ, by exploiting additional CMS measurements to constrain parton distribution functions (PDFs) that dominate the uncertainty in the original CMS forward–backward asymmetry (A_FB) analysis at √s = 13 TeV. The authors first reproduce the CMS A_FB extraction using a global χ² fit that incorporates 63 double‑differential (|y|, M) data points, nuisance parameters for experimental and theoretical systematics, and state‑of‑the‑art QCD (NNLO or approximate N³LO) and electroweak corrections (POWHEG‑Z_ew). PDF uncertainties are evaluated with 19 modern PDF sets (CT18, NNPDF40, MSHT20, etc.) via Hessian variations.

To reduce the PDF‑driven component, the analysis adds two complementary data sets: (i) the 13 TeV W‑boson charge asymmetry measurement (18 points), which tightly constrains the d/u quark ratio, and (ii) the inclusive W/Z cross‑section ratios measured at 5.02 TeV and 13 TeV (2 points), which are sensitive to the strange‑quark and photon PDFs. The combined data set contains 83 points and is fitted simultaneously with the A_FB data using the same χ² framework.

Results show a dramatic reduction of the total uncertainty. With A_FB alone, the CT18Z PDF set yields sin²θ_eff^ℓ = 0.23166 ± 0.00056. Adding the W asymmetry shrinks the error to ±0.00032, and including the W/Z ratios further reduces it to ±0.00024, giving the final value sin²θ_eff^ℓ = 0.23156 ± 0.00024. After profiling, 18 of the 19 PDF sets agree with the CT18Z central value within one standard deviation; only MSHT20 nnlo_as118 shows a modest 1.38σ deviation and a slightly larger χ².

The measured value is fully compatible with the 2025 Standard Model global fit (0.23161 ± 0.00004) and represents the most precise single determination of sin²θ_eff^ℓ to date, surpassing previous results from LHCb, ATLAS, CDF, and D0. The improved precision strengthens constraints on beyond‑Standard‑Model scenarios such as the Two‑Higgs‑Doublet Model, especially when combined with the recent CDF W‑mass measurement.

In conclusion, by integrating CMS W‑boson charge asymmetry and W/Z cross‑section ratio data into the PDF profiling, the authors effectively eliminate the dominant PDF uncertainty, achieving a sub‑0.1% measurement of the weak mixing angle. This methodology demonstrates the power of combined LHC observables to refine electroweak parameters and sets a benchmark for future high‑precision studies at the LHC and beyond.