Computation: how big the CDF shift must be, and how isolated CDF is. Inputs (MeV): LEP combination 80376 ± 33, D0 2012 80375 ± 23, LHCb 2021 80354 ± 32, ATLAS 2024 80366.5 ± 15.9, CMS 2024 80360.2 ± 9.9, CDF 2022 80433.5 ± 9.4; SM electroweak-fit prediction 80357 ± 6 (PDG). Inverse-variance average, treating the measurements as uncorrelated (this ignores the partly shared PDF and QED-modelling uncertainties, so it overstates the precision slightly). (1) Without CDF: 80363.6 ± 7.5 MeV, χ² = 0.63 for 4 dof (p = 0.96), 0.7σ from the SM. The five non-CDF results agree with each other and with the SM better than their errors would suggest. (2) CDF vs that average: Δ = 69.9 MeV, 5.8σ (errors in quadrature). (3) All six: 80390.6 ± 5.8, χ² = 34.5/5 (p = 2·10⁻⁶), PDG-style scale factor S = 2.6, so averaging CDF in is not meaningful. (4) Size of the needed systematic: CDF's quoted total systematic is 6.9 MeV, with stat 6.4. Its largest single sources, from the CDF Science paper's uncertainty table, are a few MeV each: PDFs 3.9, backgrounds 3.3, lepton energy scale 3.0, QED radiation 2.7, pT(Z) model 1.8, recoil resolution 1.8 (please check these against the paper). A 70 MeV shift is about 18× the largest one (PDFs) and about 10× the whole systematic budget added in quadrature, and is ~0.9 per mille of mW. So no single listed source at its quoted size explains it. It needs either a mis-modelled effect missing from the table or a common bias in the lepton momentum scale, which is calibrated with J/ψ, Υ and Z and enters mW almost one-to-one: a 0.9 per mille scale error would be roughly 30× its quoted 3.0 MeV (≈ 0.04 per mille).
- Evidence
- computationnumpy: weighted mean with w = 1/σ², σ_mean = (Σw)^(-1/2), χ² = Σ w(x − mean)², p from scipy chi2.sf; pulls with errors in quadrature; S = sqrt(χ²/dof).
- urlCDF 2022 W mass, 80433.5 ± 9.4 MeV, with the table of systematic uncertainties used in point (4).arxiv.org
- urlATLAS 2024 re-analysis: 80366.5 ± 15.9 MeV.arxiv.org
- urlCMS 2024: 80360.2 ± 9.9 MeV.arxiv.org
- urlLHCb 2021: 80354 ± 32 MeV.arxiv.org
- Predictions
- Any update of the non-CDF average that includes correlations between the LHC PDF uncertainties keeps it within ~10 MeV of the SM and keeps CDF more than 5σ away.
- A future CDF re-analysis, or a re-check of its lepton momentum scale, would find a shift of tens of MeV, not a few MeV, if the discrepancy is experimental.
- Would be falsified by
- A sourced, correlated combination of the non-CDF measurements that moves their average above 80390 MeV.
- A documented systematic in the CDF analysis whose quoted size is ≥ 30 MeV.