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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 advances precision determinations of the effective leptonic weak mixing angle, sin^2θ^ℓ_eff, in the Z-pole region by exploiting forward-backward asymmetries in Drell–Yan dilepton production at the LHC and by systematically constraining proton PDFs through A_4 profiling. It reproduces and extends the CMS 13 TeV analysis by incorporating additional CMS W and Z measurements (W asymmetry and W/Z cross-section ratios), achieving the most precise single measurement to date: sin^2θ^ℓ_eff = 0.23156 ± 0.00024, in excellent agreement with the SM prediction sin^2θ^ℓ_eff ≈ 0.23161(4). The study demonstrates that PDF uncertainties dominate the CMS 13 TeV result and that joint profiling with complementary measurements can substantially reduce these uncertainties, bringing the extracted value into tight concordance with the SM while highlighting the potential for future LHC measurements (including b-quark initial-state channels and running of sin^2θ^MSbar(μ) up to 3 TeV) to further test electroweak radiative corrections. The work also discusses practical outlooks for HL-LHC datasets to reach even finer precision and to probe potential beyond-SM effects in the electroweak sector.

Abstract

We review the current status and techniques used in precision measurements of the effective leptonic weak mixing angle $\sin^2θ^\ell_{\rm eff}$ (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 $\sin^2θ^\ell_{\rm eff}$ 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 $\sin^2θ^\ell_{\rm eff}$ 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 $\sin^2θ^\ell_{\rm eff}$ 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 $\sin^2θ^\ell_{\rm eff}$ 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 $\sin^2θ^\ell_{\rm eff}$, a measurement of $\sin^2θ^\ell_{\rm eff}$ for b-quarks in the initial state, and a measurement of the running of $\sin^2θ^{\overline{\rm MS}}(μ)$ up to 3 TeV.

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

TL;DR

This work advances precision determinations of the effective leptonic weak mixing angle, sin^2θ^ℓ_eff, in the Z-pole region by exploiting forward-backward asymmetries in Drell–Yan dilepton production at the LHC and by systematically constraining proton PDFs through A_4 profiling. It reproduces and extends the CMS 13 TeV analysis by incorporating additional CMS W and Z measurements (W asymmetry and W/Z cross-section ratios), achieving the most precise single measurement to date: sin^2θ^ℓ_eff = 0.23156 ± 0.00024, in excellent agreement with the SM prediction sin^2θ^ℓ_eff ≈ 0.23161(4). The study demonstrates that PDF uncertainties dominate the CMS 13 TeV result and that joint profiling with complementary measurements can substantially reduce these uncertainties, bringing the extracted value into tight concordance with the SM while highlighting the potential for future LHC measurements (including b-quark initial-state channels and running of sin^2θ^MSbar(μ) up to 3 TeV) to further test electroweak radiative corrections. The work also discusses practical outlooks for HL-LHC datasets to reach even finer precision and to probe potential beyond-SM effects in the electroweak sector.

Abstract

We review the current status and techniques used in precision measurements of the effective leptonic weak mixing angle (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 from a new analysis of the published forward-backward asymmetry () 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 published by CMS is dominated by uncertainties in Parton Distribution Functions (PDFs), which are reduced by PDF profiling using the dilepton mass dependence of . Our new extraction of from the CMS values of includes profiling with additional new CMS measurements of the -boson decay lepton asymmetry, and W/Z cross section ratio at 13 TeV. We obtain the most precise single measurement of to date of 0.231560.00024, which is in excellent agreement with the SM prediction of 0.231610.00004. We also discuss outlook for future measurements at the LHC including more precise measurements of , a measurement of for b-quarks in the initial state, and a measurement of the running of up to 3 TeV.

Paper Structure

This paper contains 11 sections, 2 equations, 12 figures, 4 tables.

Table of Contents

  1. Introduction
  2. $\sin^2\theta^\ell_{\rm eff}$ measurements in $e^+e^-$ colliders
  3. $\sin^2\theta^\ell_{\rm eff}$ measurements in hadron colliders
  4. The CMS measurement of $\sin^2\theta^\ell_{\rm eff}$ at 13 TeV
  5. PDF re-weighting/profiling
  6. A new analysis of the published CMS 13 TeV measurements of $A_4$
  7. Reproduction of the CMS 13 TeV analysis
  8. Including $W$ decay lepton asymmetry and $W/Z$ cross section ratios in PDF profiling
  9. Outlook for the future
  10. Acknowledgements
  11. Effects of PDF profiling with CMS $A_4$, $W_{\rm asym}$ and $W/Z$ ratio measurements

Figures (12)

  • Figure 1: Measurements of $\sin^2\theta^\ell_{\rm eff}$ in electron colliders (LEP, SLD) ALEPH:2005ab compared to the prediction of the 2025 SM global fit ParticleDataGroup:2024cfkPDG2025. Also shown is the prediction of the Two Higgs Doublet ModelBiekotter:2022abc corresponding to the CDF $M_W$ valueCDF:2022hxs (80.4335 $\pm$0.0094 GeV). The average of all six different LEP/SLD measurements is 0.23153$\pm$0.00016, which is in excellent agreement with the SM value. However, the $\chi^2$ is 11.5/5(dof) which may be from systematic errors which are not accounted for.
  • Figure 2: Extracted values of $\sin^2\theta^\ell_{\rm eff}$ 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 one degree of freedom corresponds to the free parameter $\sin^2 \theta^\ell_{\rm eff}$.
  • Figure 3: Values of $\sin^2\theta^\ell_{\rm eff}$ (extracted with 19 different PDF sets) before profiling compared to values after profiling with the CMS 13 TeV $A_4$ data (63 data points, left panel) and by also including the CMS $W_{asym}$ measurementCMS:2020cph at 13 TeV (18 additional data points , middle panel) and then by also including the CMS measurement of the $W$ and $Z$ cross section ratioCMS:2024myi at 13 TeV (1 additional point, right panel).
  • Figure 4: Comparison of the predictions of CT18Znnlo for $A_4(|y|,m)$, and $W_{asym}(|\eta|)$ before (red) and after (blue) full profiling.
  • Figure 5: Comparison of the predictions of 19 PDFs sets with various levels of profiling to the W/Z cross section ratios measured by CMS at 5.02 TeV and 13 TeV
  • ...and 7 more figures