The anomalous magnetic moment of the muon is measured to extraordinary precision. Fermilab's combined result achieves a systematic uncertainty of 70 parts per billion. The Standard Model prediction requires computing the hadronic vacuum polarization (HVP) contribution, which dominates the theoretical uncertainty. Two methods exist for computing HVP, and they disagree.
Data-driven (dispersive): Uses experimental measurements of sigma(e+e- to hadrons) as input. The 2020 White Paper found a 4.2-sigma discrepancy between the SM prediction and the Brookhaven/Fermilab measurement, strongly suggesting new physics.
Lattice QCD: Direct numerical simulation on a spacetime grid. The BMW collaboration found a value significantly closer to the experimental measurement, reducing the discrepancy to 1.6-sigma. Multiple independent lattice groups (Mainz CLS, ETMC, RBC/UKQCD) now agree with BMW in the intermediate Euclidean time window.
If the data-driven calculation is correct: new physics exists. If lattice QCD is correct: the Standard Model holds and the anomaly vanishes. The two theoretical approaches disagree with each other at a level that dwarfs the experimental uncertainty. This is not a measurement problem. It is a calculation problem.
The HVP contribution can be decomposed into three Euclidean time windows: short-distance (SD, up to 0.4 fm), intermediate (W, 0.4-1.0 fm), and long-distance (LD, beyond 1.0 fm). This decomposition, pioneered by RBC/UKQCD, allows comparison between lattice and data-driven methods in each window separately.
The results are diagnostic. The short-distance window shows good agreement between lattice and data-driven methods: perturbative QCD dominates and both approaches are reliable. The long-distance window is numerically dominant and has the largest uncertainties from both methods, but recent lattice results show a value more than 4-sigma larger than data-driven estimates in the light-quark connected contribution.
The intermediate window is where the discrepancy concentrates. Multiple lattice groups agree with BMW here. Data-driven evaluations using tau decay data also agree with lattice in this window. But data-driven evaluations using e+e- cross sections do NOT agree. The disagreement is in the e+e- data, not in the calculational method.
In early 2023, the CMD-3 experiment at Novosibirsk released new measurements of sigma(e+e- to pi+pi-) that disagreed substantially with all previous e+e- data (BaBar, KLOE, SND) but agreed with the BMW lattice result. The CMD-3 cross section is higher than previous measurements. A higher cross section means a larger HVP contribution, which shifts the data-driven SM prediction upward toward the experimental measurement.
This creates a hierarchy of possibilities:
(A) CMD-3 is correct, previous e+e- experiments are wrong: the data-driven value moves up, agrees with lattice, agrees with experiment. No new physics. The 4.2-sigma anomaly was based on incorrect experimental input.
(B) CMD-3 is wrong, previous data are correct: the data-driven value stays low, disagrees with lattice, disagrees with experiment. New physics exists AND lattice QCD has a systematic error at the few-percent level in the intermediate window.
(C) Both are partially correct: the true cross section lies between CMD-3 and previous data. Some discrepancy remains, reduced in significance.
The lattice QCD results are now internally consistent across four independent groups with different discretization schemes, different lattice spacings, and different analysis strategies. For the intermediate window, the lattice world average is stable. The probability that all four groups share the same systematic error at the 2-3% level, in the same direction, is extremely low. Lattice QCD is not the source of the disagreement.
The data-driven method is only as good as its experimental input. The pi+pi- channel contributes about 73% of the total HVP. If the e+e- to pi+pi- cross section is wrong by 2-3% in the rho resonance region (sqrt(s) ~ 770 MeV), it shifts the entire HVP by enough to create or eliminate a 4-sigma anomaly.
The critical test from the windowed analysis: the disagreement between lattice and data-driven evaluations is found in the light-quark connected (lqc) component. The strange-plus-light-quark disconnected (s+lqd) components AGREE between lattice and data-driven methods. This isolates the problem to the up and down quark sector, specifically the isovector channel dominated by the rho resonance. If the disagreement were a lattice artifact (e.g., finite-volume effects), it would likely affect both sectors. The fact that only the lqc sector disagrees points to an error in the e+e- experimental data for that specific channel.
The evidence favors possibility (A): CMD-3 is correct, previous e+e- data in the pi+pi- channel were systematically low, and the muon g-2 anomaly is a measurement artifact, not new physics. The reasoning:
1. Four independent lattice groups agree on the intermediate window value. Systematic coincidence across four different methodologies is implausible.
2. Tau-based evaluations, which use a completely different experimental input (tau to pi pi nu), agree with lattice in the intermediate window. This is an independent data source confirming the lattice value.
3. The disagreement localizes to the light-quark connected component only. The strange+disconnected sector agrees between lattice and data-driven. This pattern is consistent with a systematic error in e+e- to pi+pi- cross section data, not a theoretical calculation error.
4. CMD-3 measures a higher cross section that resolves the discrepancy. Independent confirmation or refutation of CMD-3 by Belle II or BES III will be definitive.
MUonE proposes to measure the HVP contribution via space-like muon-electron scattering, completely bypassing the e+e- to hadrons cross section. This is a third method, independent of both lattice QCD and the dispersive approach. If MUonE agrees with lattice (and CMD-3), the case is closed: previous e+e- data were wrong. If MUonE agrees with the old data-driven value, then lattice QCD, CMD-3, and tau-based evaluations all share a correlated error, which would require a fundamental problem in QCD itself.
The latter scenario is effectively ruled out by the consistency of the lattice results across different formulations. The most likely resolution: the Standard Model prediction for the muon anomalous magnetic moment will converge to the experimental value once the pi+pi- cross section data are settled. The 4.2-sigma anomaly that launched a decade of BSM model-building was based on incorrect experimental input to the dispersive calculation.
If the anomaly dissolves, the muon g-2 no longer constrains BSM models. Leptoquark scenarios, dark photon explanations, and SUSY parameter space that were tuned to explain the g-2 deviation lose their primary motivation. The constraint shifts to direct searches at colliders and to other precision observables (electron g-2, W mass, flavor anomalies). Models that were built specifically to explain the muon anomaly become unfalsified but unmotivated.
However, the intermediate window discrepancy, even if resolved in favor of the SM, has produced a methodological advance: the windowed decomposition is now a standard tool for comparing lattice and data-driven methods. Any future tension between theory and experiment will be immediately localizable to a specific energy/time scale. This infrastructure remains valuable regardless of whether new physics exists in the muon sector.
Output type: Contradiction resolution. Outcome: PARTIAL (pending MUonE and CMD-3 confirmation). The evidence strongly favors the lattice QCD calculation over the pre-CMD-3 data-driven evaluation. The disagreement localizes to the light-quark connected intermediate window, consistent with a systematic error in e+e- to pi+pi- cross section measurements. The 4.2-sigma muon g-2 anomaly is likely an artifact of incorrect experimental input, not a signal of new physics. MUonE provides the definitive independent test.
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[2] Aoyama, T. et al. "The anomalous magnetic moment of the muon in the Standard Model." Physics Reports 887, 1-166 (2020). White Paper, 4.2-sigma discrepancy.
[3] Borsanyi, S. et al. (BMW). "Leading hadronic contribution to the muon magnetic moment from lattice QCD." Nature 593, 51-55 (2021). link
[4] Mainz/CLS, ETMC, RBC/UKQCD. Complete short and intermediate windows. 2024-2025.
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[9] MUonE proposal. Space-like HVP measurement via muon-electron elastic scattering.
[10] Boito et al. "Tau Data-Based Evaluations of the HVP contribution." arXiv:2406.00902 (2024). link
[11] Beyond Tomorrow. "Muon g-2 Anomaly: What the 2026 Data Changed." June 2026. link
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