Precision Electroweak Measurements

The Standard Model of particle physics (SM) stands as the most precisely tested theory in scientific history, successfully describing three of the four fundamental interactions and all known elementary particles. However, the SM remains an incomplete framework, as it fails to account for gravity, dark matter, dark energy, or the observed matter-antimatter imbalance in the universe. While direct searches for “Beyond the Standard Model” (BSM) physics have yet to yield experimental confirmation of theories like supersymmetry, precision measurements offer a critical, theory-independent strategy for discovery. By over-constraining the SM’s 19 free parameters through high-accuracy measurements, we can test the theory’s self-consistency; any significant deviation from predicted theoretical relationships would serve as a clear sign of BSM effects and provide a focus for future direct searches.

W Boson Mass and Width

The global particle physics community was recently (2022) jolted by a measurement from the CDF experiment at the Tevatron, which reported a W boson mass significantly higher than the Standard Model prediction. With this result standing 7 standard deviations away from the theoretical value, it appeared for a moment that the Standard Model was “shaking,” raising the critical question of whether we were witnessing the first definitive evidence of new physics or an unresolved experimental systematic. This tension placed the attention of the entire field on whether subsequent analyses would confirm this deviation or support the established theory.

The next generation of W boson mass (m_W) and width (Γ_W) measurements at CMS will build upon the techniques developed in the efforts described below. While the current world record for m_W precision stands at 9.4 MeV from CDF and at 9.9 MeV from the most recent CMS results, the target for future analyses is an unprecedented accuracy of less than 5 MeV. This leap in precision will primarily made possible by the “universal” muon momentum calibration framework, which aims to reduce the leading systematic uncertainty, the muon momentum scale, to a relative level of 2 · 10^-5. By simultaneously fitting the W and Z boson masses along with the electroweak mixing angle, the collaboration can consistently establish experimental and theoretical correlations, effectively turning the CMS detector into a precision instrument that can test the deepest self-consistency of the Standard Model.

Z Boson Mass

The measurement of the Z boson mass (m_Z) at the Large Hadron Collider (LHC) represents a fundamental shift in experimental strategy compared to the previous era of the Large Electron-Positron Collider (LEP). At LEP, the m_Z precision was primarily dictated by the knowledge of the colliding beam energy, determined via resonant depolarization. In contrast, because the initial state partons in proton-proton collisions have unknown momenta, the LHC approach must reconstruct the mass entirely from the kinematics of the final-state decay products. Achieving a result that rivals the LEP determination was widely considered impossible just five years ago, with experts predicting that LEP’s results would stand unchallenged until a future linear collider was built. A successful m_Z measurement at CMS with a target accuracy of 2 MeV would therefore be an experimental triumph, demonstrating that advanced detector technology and innovative analysis methods can overcome the inherently “messy” environment of a hadron collider to set a new global standard.

To reach this unprecedented level of precision, the effort employs a rigorous calibration strategy that uses various particle resonances as “standard candles” to map the CMS detector’s response. By analyzing high-statistics samples of J/ψ and (Upsilon) mesons, the project determines over 100,000 alignment and calibration parameters, including the modeling of the magnetic field and detector material. This resonance-based approach is extended to include low energetic kaons or pions from B or D hadron decays and pions from displaced kaons to break correlations between parameters and obtain a universal calibration. This comprehensive framework ensures that the muon momentum is understood to a relative accuracy of approximately 2 · 10^-5 turning the CMS detector into a precision instrument that sets the baseline for other observables, such as the masses of the W and Higgs bosons.

Low pileup and the missing transverse energy calibration

As we look toward the 2026 data-taking period, a focus for the CMS collaboration is the dedicated “low pileup” (low-PU) run, heavily coordinated by our team. In the standard high-luminosity environment of the LHC, dozens of simultaneous proton-proton collisions (pileup) occur in every bunch crossing, creating a “noisy” background that complicates the reconstruction of missing transverse energy (MET), the primary signature of the neutrino in W boson decays. By operating at a significantly lower collision density, we can achieve a much cleaner environment, allowing for a far more precise understanding of the hadronic recoil and MET reconstruction. This specialized run is a crucial path toward measuring the W boson transverse momentum (p_T) and the transverse mass (m_T) with minimal systematic bias. Ultimately, these “clean room” conditions serve as a foundational step for future high-precision measurements of both the W mass and width, providing the experimental clarity needed to further stress-test the Standard Model.

Strong Coupling Constant

At the LHC the electroweak sector cannot be measured without understanding QCD. A vital objective is the new, independent determination of the strong coupling constant, α_S, based on the transverse momentum (p_T) spectrum of the Z boson. As the least precisely known of all fundamental coupling constants in the Standard Model, reducing the uncertainty of α_S is of significant importance for the broader physics program, as it serves as a primary input for nearly all cross-section predictions and enters sizably into global electroweak fits.

A recent measurement by the ATLAS collaboration achieved a precision comparable to the current world average, but the analysis faced criticism regarding the difficult theoretical description of the low-Z p_T regime, where effects such as p_T resummation, non-perturbative incoming parton momentum, and parton distribution function (PDF) uncertainties become highly relevant.

Weak Mixing Angle

Complementing the mass measurements, the team also focuses on the high-precision determination of the effective leptonic electroweak (EW) mixing angle, sin²θ_eff^ℓ. This parameter is a cornerstone of the Standard Model, as it defines the relative strengths of the electromagnetic and weak interactions. A precise measurement is of particular historical and scientific interest to resolve a long-standing discrepancy between the two most accurate results from the LEP and SLD experiments, which have differed by more than three standard deviations for decades. Recently, the CMS experiment has demonstrated the power of the LHC to address this by measuring the EW mixing angle with a relative accuracy of approximately 0.1%, providing critical new data to clarify this conflict.

.