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

Arie Bodek, Hyon-San Seo, Un-Ki Yang

TL;DR

This work presents a CMS-based determination of the effective leptonic weak mixing angle $\sin^2\theta^\ell_{\mathrm{eff}}$ using the forward–backward asymmetry in Drell–Yan events at $\sqrt{s}=13$ TeV. It introduces an extended PDF profiling strategy that combines the original $A_4$ measurement with CMS $W$-boson lepton asymmetry and $W/Z$ cross-section ratios to tighten constraints on parton densities. The analysis yields $\sin^2\theta^\ell_{\mathrm{eff}} = 0.23156 \pm 0.00024$, representing the most precise single determination to date and achieving excellent cross-PDF consistency. The results provide a stringent SM test by aligning different PDF sets with a common, high-precision electroweak parameter and demonstrate the value of integrating PDF-sensitive observables into precision fits at hadron colliders.

Abstract

This contribution presents a overview of a recent CMS-based determination of the effective leptonic weak mixing angle, $\sin^2θ^\ell_{\mathrm{eff}}$, derived from forward-backward asymmetry measurements in Drell-Yan events at 13 TeV. Although the CMS analysis achieved a major reduction in uncertainties, its overall precision is ultimately limited by residual parton distribution function (PDF) uncertainties. This proceeding highlights the role of complementary CMS observables, which probe distinct parton-density combinations and provide additional constraints beyond those obtained from the original asymmetry measurement alone. The improved analysis yields a substantially reduced total uncertainty, resulting in $\sin^2θ^\ell_{\mathrm{eff}} = 0.23156\pm0.00024$. This result is consistent with the Standard Model prediction and represents the highest precision achieved so far in an individual determination of this parameter.

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

TL;DR

This work presents a CMS-based determination of the effective leptonic weak mixing angle using the forward–backward asymmetry in Drell–Yan events at TeV. It introduces an extended PDF profiling strategy that combines the original measurement with CMS -boson lepton asymmetry and cross-section ratios to tighten constraints on parton densities. The analysis yields , representing the most precise single determination to date and achieving excellent cross-PDF consistency. The results provide a stringent SM test by aligning different PDF sets with a common, high-precision electroweak parameter and demonstrate the value of integrating PDF-sensitive observables into precision fits at hadron colliders.

Abstract

This contribution presents a overview of a recent CMS-based determination of the effective leptonic weak mixing angle, , derived from forward-backward asymmetry measurements in Drell-Yan events at 13 TeV. Although the CMS analysis achieved a major reduction in uncertainties, its overall precision is ultimately limited by residual parton distribution function (PDF) uncertainties. This proceeding highlights the role of complementary CMS observables, which probe distinct parton-density combinations and provide additional constraints beyond those obtained from the original asymmetry measurement alone. The improved analysis yields a substantially reduced total uncertainty, resulting in . This result is consistent with the Standard Model prediction and represents the highest precision achieved so far in an individual determination of this parameter.
Paper Structure (4 sections, 1 equation, 2 figures, 1 table)

This paper contains 4 sections, 1 equation, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Reproduction of the CMS 13 TeV analysis
  3. Extended Profiling with $W$ Charge Asymmetry and $W/Z$ Cross Section Ratios
  4. Conclusion

Figures (2)

  • Figure 1: Extracted values of $\sin^2\theta^\ell_{\mathrm{eff}}$ from the 13 TeV CMS $A_4$ data for 19 different PDF sets on the horizontal axis. (A) Before profiling. (B) After profiling with $A_4$. (C) After profiling with $A_4$ plus $W$ decay lepton asymmetry. (D) After profiling with $A_4$ plus $W$ decay lepton asymmetry plus W/Z cross section ratios. The vertical axis shows the $\chi^2$ values of the fits divided by the number of degrees of freedom ($N_{\rm data}-1$), where the one degree of freedom corresponds to the free parameter $\sin^2\theta^\ell_{\mathrm{eff}}$.
  • Figure 2: Comparison of $\sin^2\theta^\ell_{\mathrm{eff}}$ extracted in this analysis (labeled "This analysis 13 TeV") with previous measurements ALEPH:2005abCDF:2016ceiD0:2017ekdATLAS:2015ihyCMS:2018ktxCMS:2024onyLHCb:2015jyuLHCb:2024ygc and the prediction of the 2025 SM global fit ParticleDataGroup:2024cfkPDG2025. Also shown is the prediction of the Two Higgs Doublet Model Biekotter:2022abc corresponding to the CDF $M_W$ value CDF:2022hxs (80.4335 $\pm$0.0094 GeV).