A Parts Per Thousand Measurement Of The Electroweak Mixing Angle

The weak mixing angle or Weinberg angleis a parameter in the Weinberg–Salam theory (by Steven Weinberg and Abdus Salam) of the electroweak interaction, part of the Standard Model of particle physics, and is usually denoted as θ(W). It is the angle by which spontaneous symmetry breaking rotates the original W(0) and B(0) vector boson plane, producing as a result the Z(0) boson, and the photon. Its measured value is slightly below 30°, but also varies, very slightly increasing, depending on how high the relative momentum of the particles involved in the interaction is that the angle is used for.

- Wikipedia.

In the Standard Model of Particle Physics, the electroweak mixing angle is a function of the ratio of the W boson mass to the Z boson mass, and is also a function a simple formulas that have the electromagnetic coupling constant and the weak force coupling constant as inputs.

The electroweak mixing angle is of mostly theoretical interest as a key derived parameter in the electroweak force unification (i.e. it can be calculated from other Standard Model fundamental constants) that was a key breakthrough in the development of the Standard Model of Particle Physics. 

A part per thousand measurement honestly isn't all that precise for electroweak physics (some physical constants in electroweak physics are known to parts per million levels or better), but since it doesn't have many direct engineering applications, its measurement is mostly a consistency check on the electroweak portion of the Standard Model as a whole, that provides a fairly tight global constraint on the magnitude of beyond the Standard Model physics of many varieties that can be consistent with the experimental data (in much the same way as muon g-2 measurements do). 

But, unlike muon g-2, at least at the precisions at which we can measure it, the electroweak mixing angle only receives electromagnetic force and weak force contributions, and does not receive QCD strong force contributions.

The measurement of this physical constant described in the paper below is made at the momentum scale of the Z boson pole mass, about 91.19 GeV/c^2, which in an energy range known as the electroweak scale.

This energy scale is considerably greater than the mass-energies of first and second generation quarks, the electrons, muons, tau leptons, protons, neutrons, and the light mesons that bind protons and neutrons in atomic nuclei. But, it is considerably less the the maximum momentum scales that can be reached at the Large Hadron Collider (LHC), which is the highest energy particle collider. 

The energy scale at which this measurement is made is about three orders of magnitude higher in energy scale than the energy scale at which the anomalous magnetic moment of the muon (i.e. muon g-2) is measured, which is about 0.10566 GeV/c^2.

This contribution presents a overview of a recent CMS-based determination of the effective leptonic weak mixing angle, sin2θℓeff, 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 sin2θℓeff = 0.23156 ± 0.00024. This result is consistent with the Standard Model prediction and represents the highest precision achieved so far in an individual determination of this parameter.

Arie Bodek, Hyon-San Seo, Un-Ki Yang, "Summary of the Precision Measurements of the Electroweak Mixing Angle in the Region of the Z pole" arXiv:2601.20717 (January 28, 2026).

The value measured by the CMS experiment at the LHC is about 0.00005 lower than the Standard Model prediction (which is about 0.2 sigma and indicates that the uncertainty in the measurement is probably overstated with conservative assumptions about its accuracy).

This result, more clearly than past experimental results, favors the Standard Model of Particle Physics over the beyond the Standard Model "two Higgs doublet" model, which which there are four extra Higgs bosons, two charged Higgs bosons (positive and negative), one odd parity Higgs boson, and one heavy even parity Higgs boson. 

Earlier LHC measurements (in blue), Tevatron measurements (in green), and pre-Tevatron measurements from LEP and SLD (in black), were collectively inconclusively in their relative preferences for the Standard Model compared to a two Higgs doublet model. The CDF M(W) value below is an outlier that has never been taken very seriously, and probably the product of some sort of subtle analysis error.