W-Boson Mass Measurements and Fits

The direct $W$-boson mass measurements do not presently form one statistically coherent high-precision cluster. The 2026 CMS result agrees with ATLAS, LHCb, and the Standard Model electroweak fit, whereas CDF II remains a precise, isolated high value. That pattern disfavors treating the CDF shift as established new physics, but it also makes a naïve world average scientifically misleading.

Evidence cutoff. 11 August 2026. Reassess by 11 November 2026 or after a new official measurement, common reanalysis, or electroweak-fit update.

Required background. Electroweak precision observables explains the radiative sensitivity of $m_W$; correlated Standard Model fits supplies the global-fit logic and covariance requirements.

Helpful background. Gauge-boson masses and electroweak mixing fixes the tree-level relation; electroweak renormalization input schemes explains scheme-dependent intermediate quantities; EFT as a controlled expansion is needed before interpreting a residual as a higher-dimensional interaction.

The mass observable and its comparison class

The brief concerns running-width Breit–Wigner mass parameters inferred from transverse-mass or charged-lepton momentum spectra in hadron-collider $W\to\ell\nu$ events, compared with the Standard Model global electroweak fit. This line-shape convention is distinct from the complex-pole position, so comparisons require a common convention. The brief excludes the $W$ width, anomalous-coupling fits, and model-specific explanations of CDF II.

The extraction is not a direct invariant-mass reconstruction because the neutrino longitudinal momentum is unmeasured. Templates therefore depend on detector calibration and recoil, parton distributions, QCD radiation, electroweak corrections, and the modeled $W$ transverse momentum. Two quoted masses can share theory inputs even when the collision datasets and detectors are independent.

Evidence matrix

Source and method	Relation to the bounded claim	Independence	Result and stated uncertainty	Main limitation
CMS, 2026, 13 TeV $W\to\mu\nu$ template fit	supports compatibility with the electroweak fit; counts against a universal CDF-sized shift	new detector, energy, dataset, and analysis strategy; shares PDF and perturbative theory families with other hadron-collider analyses	$m_W=80360.2\pm9.9\ \mathrm{MeV}$	leading calibration and PDF errors remain analysis dependent
CDF II, 2022, Tevatron $W\to\ell\nu$ templates	evidence for a higher mass within the CDF analysis	independent collider and detector; reuses common electroweak and hadronic theory ingredients	$m_W=80433.5\pm9.4\ \mathrm{MeV}$	strong incompatibility with the later high-precision CMS result and the global fit remains unexplained
ATLAS, 2024, reanalysis of 7 TeV data	supports the lower-mass cluster	independent detector and calibration; LHC production and PDF systematics overlap conceptually with CMS	$m_W=80366.5\pm15.9\ \mathrm{MeV}$	less precise than CMS; common theory nuisance categories prevent simple independence
LHCb, 2022, forward $W\to\mu\nu$ spectrum	supports the lower-mass cluster in a complementary rapidity region	distinct forward acceptance gives different PDF sensitivity	$m_W=80354\ \mathrm{MeV}$ with about $32\ \mathrm{MeV}$ total uncertainty	theory and PDF uncertainties are a large part of the error
Standard Model electroweak fit quoted in CMS, 2026	predicts the comparison value from other precision inputs	indirect rather than a second direct measurement; shares $m_t$, Higgs, coupling, and theory inputs across fits	$m_W=80353\pm6\ \mathrm{MeV}$	conditional on the Standard Model and the selected global inputs

Compatibility without a misleading average

CMS, ATLAS, and LHCb are mutually compatible at their published precision and all lie near the indirect electroweak-fit value. Their agreement is more informative than a duplicate analysis because they cover different detectors, energies, acceptances, and calibration strategies. It is not complete independence: PDF sets, perturbative predictions, electroweak corrections, and some external calibration data form shared lineages.

CDF II is far enough from CMS and the fit that an inverse-variance average would have poor interpretive value. Such an average would return a precise number while hiding the question the data actually pose: which experimental or theory nuisance can account for the incompatibility? A defensible combination needs a common likelihood or, at minimum, harmonized definitions and cross-experiment covariance for PDFs, recoil, QED radiation, and calibration.

The present evidence therefore favors the Standard Model neighborhood but does not identify the source of CDF’s shift. “CDF is wrong” is stronger than the evidence; “the $W$ mass proves new physics” is much stronger still.

What this evidence does not establish

• Agreement with the global fit does not test the Standard Model independently of every other precision input.
• Multiple LHC measurements should not be counted as fully independent when their PDF and perturbative uncertainties share a source.
• A single mass residual cannot select a SMEFT operator without a correlated fit to other observables and a declared truncation order.
• The absence of a justified combined value is not evidence that the quoted running-width mass convention is ambiguous at the stated precision.

What would change the assessment

A reanalysis that reproduces the CDF II templates with public nuisance correlations and isolates a concrete bias would resolve the present pattern toward the lower cluster. Conversely, a comparably precise independent measurement in a different detector or kinematic regime near $80433\ \mathrm{MeV}$ would make the high-mass interpretation materially stronger.

The highest-value intermediate tests are common PDF eigenvector studies, generator and recoil comparisons using the same fiducial observables, charge- and rapidity-split fits, and released likelihood information that permits correlations to be propagated rather than guessed.

Source selection

The finite set includes every published direct hadron-collider determination needed to represent the present incompatibility and the current indirect fit quoted by the most precise recent measurement. Conference combinations, phenomenological new-physics scans, and simple averages without covariance were excluded. Numerical values are the collaborations’ published results, not a recomputation.

Related research pages

• EFT inference, power counting, and truncation for controlled interpretation of precision residuals.
• Amplitudes and precision scattering for template and perturbative uncertainty culture.
• Electroweak vacuum stability for a distinct Standard Model inference problem that should not be conflated with this one.

References

• ATLAS Collaboration. “Improved Measurement of the $W$ Boson Mass Using $7\ \mathrm{TeV}$ Proton–Proton Collisions with the ATLAS Detector.” European Physical Journal C 84 (2024): 1309. DOI.
• CDF Collaboration. “High-Precision Measurement of the $W$ Boson Mass with the CDF II Detector.” Science 376 (2022): 170–176. DOI.
• CMS Collaboration. “High-Precision Measurement of the $W$ Boson Mass with the CMS Experiment.” Nature 652 (2026): 321–327. DOI.
• LHCb Collaboration. “Measurement of the $W$ Boson Mass.” Journal of High Energy Physics 01 (2022): 036. DOI.