Muon g-2 Theory Initiative update
Physics Reports 1143, 1-158. arXiv:2505.21476. DOI:10.1016/j.physrep.2025.08.002. Exact consortium author list at the record.
Particle physics / a live uncertainty ledger
The Gap That Changed Sides
The final muon measurement did not retreat toward the Standard Model. The reference calculation changed. Operate the comparison, then open the electron-positron evidence that still refuses to become one number.
The anomaly is aμ = (gμ - 2) / 2. Every large number below is that anomaly, never g - 2 itself.
Move the reference
Three theory positions, two experimental summaries, and one deliberately missing result. All arithmetic is evaluated in your browser from the displayed inputs.
Standard Model reference
2025 lattice-based Initiative update
Difference Δ× 10-11
Combined σ× 10-11
Δ / σstandard deviations
NO CONSENSUS VALUE
The 2025 Initiative judged the electron-positron inputs too inconsistent for a meaningful combined dispersive estimate. This position fails closed and will not manufacture a current z score.
CMD-3-based 2π HVP× 10-11
Earlier data average× 10-11
Naive independent zdisplay calculation only
The 5260 benchmark uses CMD-3 where it has coverage and other data elsewhere. The naive calculation above assumes independent quoted errors and is not a CMD-3 collaboration significance.
A z score from this panel is a Gaussian display model. Independent mode combines uncertainties in quadrature. User ρ mode applies the displayed covariance formula; neither mode proves that theory systematics are Gaussian.
Is this only bookkeeping?
No committee switch can settle incompatible cross sections. This workbench integrates the pion form-factor values published in CMD-3 Table V. It is a transparent raw proxy, not the collaboration analysis.
Raw window proxy
× 10-10
|Fπ|²cumulative proxyselected window
K(s) = ∫₀¹ dx x²(1-x) / [x² + (1-x)s/mμ²]
R2π(s) = β³|Fπ(s)|² / 4
aμ = α²/(3π²) ∫ ds K(s)R(s)/s
Published RHO2013 window0.6 to 0.88 GeV, × 10-10
Published RHO2018 window0.6 to 0.88 GeV, × 10-10
Published combined window0.6 to 0.88 GeV, × 10-10
The raw browser proxy uses published |Fπ|² points, linear or step interpolation, and central constants. It does not reproduce vacuum-polarization undressing, final-state radiation, the full covariance treatment, exact 0.6 GeV endpoint coverage, or data outside the table. The published comparison above is the benchmark, not a target silently fitted by this code.
Nothing up the sleeve
Open any row. Values in green are recomputed on this page, not pasted results.
Current difference and significance:
Historical cross-era diagnostic:
Correlation convention:
σΔ² = σexp² + σtheory² - 2ρσexpσtheory. Independent mode fixes ρ = 0. The slider is constrained to -0.95 through 0.95 so the variance remains positive for the displayed inputs.
Experiment labels and unit conversion:
Naive CMD-3 comparison:
Dispersion constants and method:
α = 1 / 137.035999177, mμ = 105.6583755 MeV, and mπ± = 139.57039 MeV. The kernel integral uses composite Simpson quadrature. The energy integral uses Simpson quadrature over an interpolated Table V curve.
Corrections and covariance: declared omissions
No vacuum-polarization undressing or final-state-radiation correction is applied to the raw form-factor proxy. A complete bin covariance matrix is not embedded, so uncertainty propagation is not offered. CMD-3's full 5260(42) benchmark also uses non-CMD-3 data outside its measured region.
Data checksum:
The verifier hashes the normalized embedded Table V arrays with SHA-256 and checks the source row count, energy endpoints, and benchmark integrals. This compact browser label is a live FNV-1a fingerprint of the same arrays.
Compatibility is not closure
The lattice-based Standard Model prediction and final experiment are compatible. The electron-positron route remains unsettled because CMD-3 disagrees with important earlier two-pion measurements. The unresolved work is to locate experimental, radiative-correction, or analysis sources of those differences and to understand remaining method-by-method HVP differences.
A later 2026 hybrid lattice and low-energy-data calculation reported 715.1(2.5)(2.3)[3.4] × 10-10 for leading-order HVP and a Standard Model comparison 0.5 standard deviations from experiment. It postdates the 2025 Initiative averaging decision, so it belongs here as an epilogue, not retroactively inside that average.
Sources and status
Final Fermilab measurement
Muon g-2 Collaboration, Physical Review Letters 135, 101802. arXiv:2506.03069. DOI:10.1103/7clf-sm2v. Exact collaboration list at the record.
Earlier Theory Initiative reference
Physics Reports 887, 1-166. arXiv:2006.04822. DOI:10.1016/j.physrep.2020.07.006. Exact consortium author list at the record.
Original BMW lattice result
Sz. Borsanyi et al., exact author list at the record, Nature 593, 51-55. arXiv:2002.12347. DOI:10.1038/s41586-021-03418-1.
CMD-3 pion form factor
Physical Review D 109, 112002. arXiv:2302.08834. DOI:10.1103/PhysRevD.109.112002. Table V supplies the embedded points.
CMD-3 full two-pion benchmark
Physical Review Letters 132, 231903. arXiv:2309.12910. DOI:10.1103/PhysRevLett.132.231903. Exact collaboration list at the record.
Data-driven tensions
M. Davier, A. Hoecker, A. M. Lutz, B. Malaescu, and Z. Zhang, European Physical Journal C 84, 721. arXiv:2312.02053. DOI:10.1140/epjc/s10052-024-12964-7.
Review of Particle Physics
D. W. Hertzog and M. Hoferichter, review 56 in the 2026 PDG review. Muon anomalous magnetic moment review.
Hybrid HVP calculation
Nature 653, 373-377. arXiv:2407.10913. DOI:10.1038/s41586-026-10449-z. Exact author list at the record.